How Many Numbers Can You See? The 230 Detailed Answer

Simple game level 121

All numbers are visible, enter “0123456789”.

Easy Game Solutions [ALL LEVELS]

Easy Game Level 121 Answer

In this post you will get the answers and walkthrough of Easy Game Level 121. What number can you see?

Easy Game is a free tricky puzzle game that requires you to use your intelligence to pass the levels. Playing this game can make you smarter and make you think faster or broader. This game will challenge you with levels that will improve your memory, calculation power, reaction time, attention and many other skills.

You can play this game when you are bored alone, hanging out with family and friends, waiting for the bus at the bus stop or basically any state of mind where all you need is your brain.

Easy Game Level 121 Video Walkthrough

If you read the answer and couldn’t figure out how to solve it. Here is a video walkthrough of the level:

Easy Game Solutions [ALL LEVELS]

Brain Test Level 90 Answer: Please turn on all the lights

Tap on all buttons, two of them light up. Replace the other one from the screen. Then all the bulbs will light up.

Brain Test Answers (All Levels)

Brain test level 90 video walkthrough

If you read the answer and couldn’t figure out how to solve it. Here is a video walkthrough of the level:

In this post you will get the answers and walkthrough of Brain Test Level 90 Please turn on all the lights.

One of the best ways to fill your free time and kill your boredom is by playing Brain Test puzzles. Brain Test offers you many different tricky riddles that will make your mind work. Each level has its own solution and in each level you will get hints and hints to solve the level. Not all answers are expected to be solved as is, so you’ll have to think outside the box. The game also has a feature that can help you solve the text. If you still don’t know how to solve the level, we are here to help you.

Brain Test Answers (All Levels)

Editor’s Note: This article was originally published on April 1, 2022

People have found a new optical illusion to obsess over. A seemingly simple image shared by Twitter user @benonwine shows a number partially hidden within a black and gray striped circle. “Do you see a number? If so, which number?” they ask in the tweet. What initially seems like a fairly simple task, you quickly realize that the zigzag pattern of the circle makes things a bit tricky. Thousands of netizens from around the world have watched the visual puzzle since it was posted to Twitter, and have been amazed at how many have come to very different conclusions about the hidden figures.

do you see a number

If yes, which number? pic.twitter.com/wUK0HBXQZF – Benonwine (@benonwine) February 16, 2022

Chances are, the number 2 caught your eye almost immediately. You might also be able to spot a “528” or “4528” without straining your eyes too much. Many said the number was “45283,” while some others claimed they saw the number as “15283.” As it turns out, the correct answer is seven digits. A closer look reveals that the number reads “3452839,” a fact that stunned many Twitter users who couldn’t make out more than 3 digits within the swirling circle.

“45 283… and what’s the catch? Should I make an appointment with my GP?” asked @PhilippeAuclair. “3452839. Can some people actually not see the ending numbers even when pointed out?” @NickEd82 tweeted. “3452839. Curiously, this is also the phone number of an apartment in Islington where Arthur Dent went to a costume party and met a very nice young woman who he totally screwed up with…” commented @citysleuth. “Oddly enough, when I click reply and it shows me a thumbnail, it’s much clearer. Because it doesn’t move I guess? Anyway, 3452839 BUT 528 was clear, 45283 was more visible in some lights than others, and the 3 & 9 at the ends were hard to see at all,” @chronicleflask tweeted.

“I suspect the numbers you see depend on your ‘contrast sensitivity’ (unlike what a standard eye measures). It can be tested by opticians. It’s worth it if you’re struggling as it can affect your vision at night or in the rain, fog, etc,” @LittleToRelate helpfully explained. According to Vision Center, contrast sensitivity is “the ability to distinguish between an object and the background behind it.”

“Contrast sensitivity is distinct from visual acuity, which measures how clear your vision is at a given distance. High spatial frequencies make up detailed features like sharp edges, facial features, and the like. Low spatial frequencies are more like rough images, where you can see the overall shape of something but no detailed features. A contrast sensitivity test measures how well you can tell the difference between light and dark,” the site continues. “For this, your doctor uses a different type of chart, where the characters gradually fade from black to gray. Visual acuity is measured when You read the visual chart during an exam This is considered a high contrast test (black letters on a white You can have excellent visual acuity but reduced contrast sensitivity and vice versa.”

Makes sense – I asked the optometrist as I have trouble driving in the dark and rain – Cllr Kate Chinn 💙 🇪🇺 (@Epsom_Chinn) February 17, 2022

For safety reasons, good contrast sensitivity is required when driving in low visibility conditions such as rain, fog, low light or glare from a light source. “Numerous studies have shown that contrast sensitivity is a better indicator of driver visual performance than visual acuity. Contrast sensitivity helps you see road signs, pedestrians, curves in the road, and the difference between the road and the pavement,” the website reads. “A contrast sensitivity deficit greatly increases the likelihood of suffering an accident.” What did this optical illusion tell you about your contrast sensitivity?

Optical Illusions: Optical illusions are fun because they put our brains and eyes to the test. You can’t scroll through them without being entertained. Agree?

Recently, a seemingly simple optical illusion has taken the internet by storm. “Do you see a number? If so, what number?” the Benowine Twitter post said.

The user shared optical illusion has black and white stripes with different numbers hidden in the circle. The uneven spirals in the image created an optical illusion and made it difficult to guess the correct order.

The post, which garnered over 3,000 likes, prompted people to share the numbers they saw in the optical illusion. Some commented 528, others 45283. What numbers do you see?

do you see a number

If yes, which number? pic.twitter.com/wUK0HBXQZF – Benonwine (@benonwine) February 16, 2022

One user even shared a trick to finding the right sequence. All you have to do is pull down the notification bar. This will blur your screen and make the numbers easy to read.

Another trick is to move away from your screen or zoom the image to see the numbers clearly.

If you still can’t find the right answer, we’ll reveal it for you. The correct answer is 3452839!

The numbers your eyes see are based on your contrast sensitivity, which is the extent to which your eyes can distinguish between an object and its background.

“Sometimes our brain gets confused by what our eyes are trying to tell it,” writes the Queensland Brain Institute in a blog post.

While many scientists have tried to understand how optical illusions work, no one is sure how our brains and eyes work together to create these illusions.

Also read |

Optical Illusion: What you see in the first 30 seconds reveals whether you have a creative or logical mind

Optical illusion: only 2% can recognize two animals in the picture within 20 seconds, right?

A hidden number can also be referred to as a “private number” – or any call that rings but doesn’t display the number. Unfortunately, hidden numbers cannot be identified by Truecaller.

However, you can block any number that shows up as “Unknown” or “Private” with our powerful blocking feature. Navigate to Truecaller > > Settings > Block > Enable Hidden Number Block.

There is no greatest, last number… except infinity. Except infinity isn’t a number. But some infinities are literally larger than others. Let’s visit some of them and count past them.

Video Source: Vsauce / YouTube.

Hey Vsauce! Michael here.

What’s the biggest number you can think of? A googol? A Goolplex? A million oplex? Well, in reality, the largest number is 40.

These 40, made up of strategically planted trees in Russia, cover more than 12,000 square meters of earth and are larger than the battalion markings on Signal Hill in Calgary, the 6 on the Fovant badges in England – even the mile from Pi Brady unrolled on Numberphile . 40 is the largest number by area… on Earth.

But in terms of the set of things we usually mean by a number being “big,” 40 is probably not the biggest. For example, there’s 41. Oh, and then there’s 42 and 43…a billion, a trillion; You know, no matter how big you can think of a number, you could always go higher.

So there is no greatest, last number… except infinity? no Infinity is not a number. Instead, it’s a number of sorts. You need infinite numbers to talk about and compare infinite amounts, but some infinite amounts—some infinities—are literally larger than others. Let’s visit some of them and count past them.

The important things first. When a number refers to how many things there are, it’s called a “cardinal number.” For example 4 bananas. 12 flags. 20 points. 20 is the “cardinality” of this point set. Now two sets have the same cardinality if they contain the same number of things. We can demonstrate this equality by matching each member of one set one-to-one with each member of the other. Same cardinality, pretty straightforward.

We use the natural numbers—that is, 0, 1, 2, 3, 4, 5, and so on—as cardinal numbers when we talk about how many things there are, but how many natural numbers are there? It cannot be a natural number, since it is always followed by a 1 plus this number. Instead, there is a unique name for this set: “aleph-null” (ℵ 0 ). Aleph is the first letter of the Hebrew alphabet and aleph-zero is the first smallest infinity. There are so many natural numbers. It’s also how many even numbers there are, how many odd numbers there are; it’s also how many rational numbers — that is, fractions — there are. This may sound surprising since fractions appear more numerous on the number line, but as Cantor has shown, there is a way to arrange every single possible rational element in such a way that the natural fractions can be brought into one-to-one correspondence with them . They have the same cardinality.

The point is, aleph-zero is a large crowd; larger than any finite set. A googol, a googolplex, a googolplex factorial to the power of a googolplex to a googolplex squared Graham’s number? Aleph zero is larger. But we can calculate beyond that. As? Well, let’s use our old friend, the Super Task. If we draw a series of lines and each next line is a fraction of the size and distance of each last line, we can fit an infinite number of lines into a finite space. The number of lines here is equal to the number of natural numbers that exist. The two can be matched one to one. There’s always a Next Natural, but there’s also always a Next Line. Both sets have cardinality Aleph-zero.

But what happens if I do this? How many lines are there now? Aleph-zero plus one? no Infinite amounts are not like finite amounts. Here there are still only aleph zero lines because I can match the nature characters one to one like before. I’ll just start here and then continue from the beginning. Obviously the number of rows has not changed. I can even add two more lines, three more, four more – I always end up with aleph-zero things. I can even add another infinite aleph zero of rows and still not change the amount. Any even number can pair with these and any odd number with these. There’s still a line for every natural.

Another cool way to see that these lines don’t contribute to the grand total is to show that you can create the same sequence without drawing new lines at all. Just take every other row and move them all together to the end. That is the same.

But wait a second. This and this may contain the same number of things, but they clearly have something different, right? I mean, if it’s not about how many things they’re made of, what is? Well, let’s go back to having only one line after an aleph null collection. What if, instead of matching the Naturals one-to-one, we insisted on numbering each line according to the order in which it was drawn? So we need to start here and number from left to right. Now, what number does this line get? In the realm of infinity, putting things in order is very different from counting them. You see, this line doesn’t add to the total, but to label it according to the order in which it appeared, we need a series of labels of numbers that go beyond the natural numbers. We need ordinal numbers.

The first trans-finite ordinal is omega (ω), the lowercase Greek letter omega. This isn’t a joke or trick, it’s literally just the next label you need after first using up the infinite collection of each and every counting number. If you get ωth place in a race, that would mean infinitely many people have finished the race, and then you’ve made it. After ω comes ω+1, which doesn’t really look like a number, but it is, just like 2 or 12 or 800. Then comes ω+2, ω+3…ordinal numbers mark things in order. Ordinal numbers aren’t about how many things there are, but rather they tell us how those things are arranged—their order.

The ordinal type of a set is only the first ordinal number, which is not needed to sequentially identify everything in the set. Cardinality and order type are therefore the same for finite numbers. The ordering type of all naturals is ω. The order type of this sequence is ω+1, and now it is ω+2. No matter how long an arrangement becomes, as long as it is ordered, as long as each part of it contains an initial element, the whole describes a new ordinal number. Always. This will be very important later.

It should be noted at this point that if you ever play a game of who can name the largest number, you should be cautious and consider saying “Omega plus one”. Your opponents may require that the number you mention is a cardinal number that refers to an amount. These numbers refer to the same amount of stuff, just arranged differently. ω+1 is not larger than ω, it just comes after ω.

But Aleph-Zero is not the end. Why? Well, because it can be shown that there are infinities greater than aleph-zero that literally contain more things. One of the best ways to do this is with Cantor’s diagonal argument. In my episode on the Banach-Tarski paradox, I used it to show that the number of real numbers is greater than the number of natural numbers. But for the purposes of this video, let’s focus on another thing that’s bigger than aleph-zero: the power set of aleph-zero.

The power set of a set is the set of all the different subsets that can be made of it. For example, I can make the set of 1 and 2 a set of nothing, or 1, or 2, or 1 and 2. The power set of 1,2,3 is: the empty set, 1 and 2, and 3 and 1 and 2 and 1 and 3 and 2 and 3 and 1,2,3. As you can see, a power set contains many more members than the original set. Two to the power of how many members the original set had, to be precise. So what is the power of all that is natural?

Alright, let’s check. Imagine a list of all natural numbers. Cool. Now the subset of all, say, even numbers would look like this: yes, no, yes, no, yes, no, and so on. The subset of all odd numbers would look like this. Here’s the subset of just 3, 7, and 12. And how about any number – except 5. Or no number – except 5. Obviously, this list of subsets will be, well, infinite. But imagine matching them all one-to-one with a natural. If even then there is a way of continuing to produce new subsets that are clearly nowhere listed here, we know we have a set with more members than there are natural numbers—an infinity greater than aleph-zero.

The way to do this is to start here in the first subset and just do the opposite of what we see. 0 is a member of this, so our new set will not contain 0. Next, move diagonally down to the membership of 1 in the second subset. 1 is a member of it, so it won’t be in our new one. 2 is not in the third subset, so it will be in ours, and so on. As you can see, we are describing a subset that, by definition, differs in at least one respect from every single other subset on this aleph-zero-sized list. Even if we reinsert this new subset, diagonalization can still be performed.

The naturals power law will always resist a one-to-one correspondence with the naturals. It is an infinity greater than Aleph-Zero. Repeated applications of power sets create sets that can’t be brought into one-to-one correspondence with the last, so it’s a great way to quickly create larger and larger infinities. The point is that there are more cardinals after Aleph Zero. Let’s try to reach them.

Now remember that after ω the ordinals divide and these numbers are no longer cardinals. They don’t refer to any larger amount than the last cardinal we reached – but maybe they can get us to one. Wait… what do we do? Aleph zero? Omega? Come on, we’ve been using these numbers like there’s no problem, but if you can always add one down here at some point – always – can we really talk about this endless process, as a whole, and then follow something along with it?

Of course we can. This is math, not science! The things we assume to be true in mathematics are called axioms, and an axiom we make up is no more likely to be true if it better explains or predicts what we observe. Instead, it’s true because we say it is. Their consequences simply become what we observe. We do not adapt our theories to a physical universe whose behavior and underlying laws would be the same whether we were here or not; we create this universe ourselves. If the axioms we profess to be true lead us to contradictions or paradoxes, we can go back and adjust them, or just abandon them altogether, or we can simply refuse to allow ourselves to do things that cause the paradoxes. That’s it. What is fascinating, however, is that by ensuring that the axioms we accept do not lead to problems, we have turned mathematics into what the saying goes: “unduly effective in science”. To what extent we invent or discover all this – it is difficult to say. All we have to do to get ω is say “let there be omega” and it will be fine.

This is what Ernest Zermelo did in 1908 when he included the axiom of infinity in his list of axioms for mathematical problems. The axiom of infinity is simply the declaration that there is an infinite set – the set of all natural numbers. If you refuse to accept it, that’s okay—it makes you a finitist, someone who believes that only finite things exist. But if you accept it, as most mathematicians do, you can go quite far – past these and through these… finally we get to ω + ω, except we’ve reached another upper bound. Going all the way out to ω + ω would mean creating another infinite set, and the axiom of infinity only guarantees that this one exists.

Do we have to add a new axiom every time we describe aleph-zero-more numbers? no The axiom of substitution can help us here. This assumption says that if you take a set – such as the set of all natural numbers – and replace each element with something else – such as bananas – then there is also a set left over. It sounds simple, but it’s incredibly useful. Try this: Take every atomic number up to ω, then prefix each with “ω+” instead of bananas. Now we have reached ω+ω or ω×2. We can make jumps of any size with the replacement, as long as we only use numbers that we have already reached. We can replace any atomic number up to ω by omega times to get ω × ω , ω2. We’re cooking now! The replacement axiom allows us to construct endless new ordinal numbers. Eventually we get to ω to ω to ω to ω to ω… and we run out of standard mathematical notation. No problem! This is simply called “epsilon zero” (ε 0 ), and we continue from here.

But now think about all those ordinals. All the different ways of arranging aleph zero things. Well, these are well-ordered, so they have an order type – an ordinal number that comes after all. In this case, this atomic number is called “omega one” (ω1). Now, since ω 1 by definition comes after every single order type or aleph-zero thing, it must describe an array of literally more things than the last aleph. I mean, if not, it would be in here somewhere – but it’s not. The cardinal number describing the set of things used to make an agreement with order type ω 1 is “aleph-one” (ℵ 1 ).

It is not known where Naturals’ power law lies on this line. It cannot be between these cardinals because there are no cardinals between them. It might as well be Aleph-One – this belief is called the Continuum Hypothesis. But it could also be bigger; we just don’t know. The continuum hypothesis, by the way, is probably the biggest unanswered question in this entire topic, and today, in this video, I won’t solve it – but I will go higher and higher, to ever greater infinities.

Now, using the axiom of substitution, we can take any ordinal number we’ve already reached—such as ω—and jump from aleph to aleph to aleph-omega. Or heck why not use a larger atomic number like ω2 to construct aleph omega square? Aleph-omega-omega-omega-omega-omega-o… Our notation here only allows me to add countably many omegas, but replacing doesn’t care if I have a way of writing the numbers it achieves. Wherever I land there will be a location with even greater numbers, allowing me to make even bigger and more numerous jumps than before. The whole thing is a wildly accelerating feedback loop of embiggening. We can go on like this and reach ever greater infinities from below.

Replacements and repeated power sets, which may or may not match the Alephs, can keep our ascension going forever. So there’s clearly nothing beyond that, is there? Not so fast. That’s what we said about transcending the finitude of Omega. Why not accept as an axiom that there is a next number so large that no amount of replacement or power adjustment on anything smaller could ever get you there. Such a number is called an “unreachable cardinal” because you cannot reach it from below.

Interestingly, within the numbers we have already reached there is a shadow of such a number: Aleph-Zero. This number cannot be reached from below either. All numbers less than it are finite, and a finite number of finite numbers cannot be added finitely often, multiplied, raised to the power, replaced by finite jumps, or even raised to the power finitely often to give you anything other than another finite set. Sure, the power of a millimillion to a googolplex to a googolplex to a googolplex is really big – but it’s still only finite. Not even close to aleph zero, the first smallest infinity. Because of this, Aleph zero is often considered an inaccessible number. However, some authors don’t and say an inaccessible must also be uncountable, which, okay, makes sense – I mean, we’ve already accessed aleph-null, but remember we could only do it by using it directly declare existence axiomatic. We must do the same for inaccessible cardinals.

It’s really hard to convey the unfathomable greatness of an inaccessible cardinal. I’ll leave it at that: The conceptual leap from nothing to the first infinite is like the leap from the first infinite to the unattainable. Set theorists have described numbers greater than unattainable, and each requires a new grand cardinal axiom that confirms their existence and extends the height of our number universe. Will there ever come a point when we make an axiom that implies the existence of so many things that it implies contradictory things? Will we one day answer the continuum hypothesis? Maybe not, but there are promising directions, and until then, the amazing fact remains that many of these infinities – maybe all – are so large that it’s not exactly clear whether they even really exist or could be shown in the physical universe. If they do, if physics finds a use for them someday, that’s great – but if they don’t, that’s great too. That would mean that with this brain, a tiny thing a trillion times smaller than the tiny planet it lives on, we have discovered some truth outside of the physical realm. Something that applies to the real world, but is also strong enough to go further, beyond what the universe itself can contain or show us or be.

And as always, thanks for watching.

Another interesting fact about trans-finite ordinals is that the arithmetic with them is a little different. Usually 2+1 is the same as 1+2, but ω+1 is not the same as 1+ω. One plus omega is actually just omega. Think of them as order types: a thing placed in front of omega simply consumes all naturals and leaves us with order type omega. A thing placed after omega requires every integer and then omega, leaving us with omega plus one as the ordering type.

What is infinity?

Infinite… …it’s not big… …it’s not huge… …it’s not enormous… …it’s not extremely enormous… … it is …

Endless!

Infinity has no end

Infinity is the idea of ​​something that has no end.

In our world we don’t have anything like that. So we imagine traveling ever further and struggling to get there, but it’s not really infinite.

So don’t think like that (it will only hurt your brain!). Just think of “endless” or “limitless”.

If there is no reason that something should stop, then it is infinite.

Infinity doesn’t grow

The infinity is not “growing”, it is already fully formed.

Sometimes people (including me) say it “just keeps going,” which sounds like it’s growing somehow. But infinity doesn’t do anything, it just is.

Infinity is not a real number

Infinity isn’t a real number, it’s an idea. An idea of ​​something without end.

Infinity cannot be measured.

Even these distant galaxies cannot compete with infinity.

Infinity is easy

Yes! It’s actually easier than things that come to an end. Because if something has an end, we have to define where that end is.

Example: In geometry, a line has infinite length. A line goes in both directions without end. When there is one end it is called a ray and when there are two ends it is called a line segment but they need additional information to define where the ends are. So a line is actually simpler than a ray or a line segment.

Further examples: {1, 2, 3, …} The sequence of natural numbers never ends and is infinite. OK, 1/3 is a finite number (it’s not infinite). But written as a decimal, the digit 3 repeats itself forever (we say “repeating 0.3”): 0.3333333… (etc.) There’s no reason the 3’s should ever stop: they repeat indefinitely. 0.999… So when we see a number like “0.999…” (i.e. a decimal number with an infinite series of 9’s), there is no end to the 9’s. You can’t say “but what if it ends in an 8?” because it just doesn’t end. (Therefore 0.999… equals 1). AAAA… An infinite series of “A” followed by a “B” will NEVER have a “B”. There are infinitely many points in a line. Even a short line segment has an infinite number of points.

Big Numbers

There are some really impressively large numbers.

A googol is 1 followed by a hundred zeros (10100):

10,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000

A googol is already larger than the number of elementary particles in the known universe, but then there’s the googolplex. It’s 1 followed by googol zeros. I can’t even write down the number because there isn’t enough matter in the known universe to form all the zeros:

10,000,000,000,000,000,000,000,000,000,000,000,000, … (Googol number of zeros)

And there are even bigger numbers that “Power Towers” need to use to write them down.

For example, a googolplex can be written as this power tower:

That’s ten to the power of (10 to the power of 100),

But imagine an even larger number like (who is a Googolplexian).

And we can easily create much larger numbers than this!

Finite All these numbers are “finite”, we could eventually “get there”. But none of these numbers is anywhere near infinite. Because they are finite, and infinity is… not finite!

Use infinitely

We can sometimes use infinity as if it were a number, but infinity doesn’t behave like a real number.

For better understanding, think “infinite” when you see the “∞”:

Example: ∞ + 1 = ∞ It says that if something is endless, we can add 1 and it’s still endless. But be careful with ∞ in equations! Let’s try subtracting ∞ from both sides: ∞ − ∞ + 1 = ∞ − ∞ 1 = 0 Oh no! Something is wrong here. In fact, ∞ − ∞ is undefined. To avoid such mistakes: imagine each ∞ has a different value

We don’t know how big infinity is, so we can’t say that two infinities are equal:

Example: Even numbers The set of natural numbers {1, 2, 3, …} can be compared one-to-one with the set of even numbers {2, 4, 6, …} as follows: Both sets are infinite (endless), but one seems to be twice the size of the other!

Characteristics

The most important thing about infinity is:

-∞ < x < ∞ where x is a real number What is a mathematical abbreviation for "negative infinity is less than any real number, and infinity is greater than any real number" Here are some more properties: Special Properties of Infinity ∞ + ∞ = ∞ - ∞ + - ∞ = - ∞ ∞ × ∞ = ∞ - ∞ × - ∞ = ∞ - ∞ × ∞ = - ∞ x + ∞ = ∞ x + (- ∞ ) = - ∞ x - ∞ = - ∞ x − (- ∞ ) = ∞ For x >0 : x × ∞ = ∞ x × (- ∞ ) = -∞ For x <0 : x × ∞ = -∞ x × (- ∞ ) = ∞ Undefined operations All these are "undefined": "Undefined" operations 0 × ∞ 0 × - ∞ ∞ + - ∞ ∞ - ∞ ∞ / ∞ ∞ 0 1 ∞ Example: Is ∞∞ equal to 1? No, because we cannot say that two infinities are equal. For example ∞ + ∞ = ∞, so ∞∞ = ∞ + ∞∞ which looks like this: 11 = 21 And that doesn't make any sense! So we say that ∞∞ is undefined. Infinite Amounts If you delve further into this topic, you will find discussions about infinite sets and the idea of ​​different sizes of infinity. This subject has special names like aleph-zero (like many natural numbers), aleph-one, and so on, which are used to measure the size of sets. For example, there are infinitely many integers {0, 1, 2, 3, 4, ...}, but there are more real numbers (such as 12.308 or 1.1111115) because there are infinitely many possible variations after the decimal point, which is fine . Or think of it this way: unlike integers, we can always discover new real numbers between other real numbers, no matter how small the gap. But this is an advanced topic and goes beyond the simple concept of infinity that we are discussing here. Conclusion Infinity is a simple idea: "endless". Most things we know have an end, but infinity does not.

Metric numbers

(See also Metric/Imperial Conversion Tables and Unit Converters)

What is Kilo, Mega, Giga, Tera… ?

In the metric system, there are standard ways of talking about large and small numbers:

“kilo” for thousand,

“mega” for a million,

and more …

Example: A long rope is a thousand meters long. It is easier to say that it is 1 kilometer long and even easier to write it down as 1 km.

So we used kilo before the word meter to make “kilometre”.

And the abbreviation is “km” (k for kilo and m for meter, taken together).

Some more examples:

Example: you put your bag on a scale and it shows 2000 grams, we can call that 2 kilograms or just 2 kg.

Example: teaspoon A teaspoon holds 5 thousandths of a liter (51000 liters), but it’s better to say “5 milliliters” or just write 5 ml.

“kilo”, “mega”, “milli”, etc. are called “prefixes”:

prefix: a piece of word that can be added to the beginning of another word to form a new word

So if you use the prefix “milli” before “liter”, a new word “milliliter” is created.

Here we list the prefix for commonly used large and small numbers:

Common big and small numbers

Name The number prefix Symbol trillion 1,000,000,000,000 tera T billion 1,000,000,000 giga G million 1,000,000 mega M thousand 1,000 kilo k hundred 100 hecto h ten 10 deca da unit 1 tenth 0.1 deci d hundredth 0.01 centi k Thousandth 0.001 millim0 billionth 0.00 microth billionth 0.00 millith 000 001 nano n trillionth 0.000 000 000 001 pico p

Remember for large values ​​(each a thousand times larger): “kilo mega giga tera” and for small values ​​(each thousand times smaller): “milli micro nano pico”

Try to do something yourself!

How do you say a million liters?

How about a billionth of a meter?

At the bottom of this page are more questions to challenge yourself with…

How tall are you?

There are many differences between them. Think in time:

A million seconds is about 12 days

A billion seconds is about 32 years

A longer list:

A thousand seconds is about a quarter of an hour

Seconds is about a million seconds is about 12 days

Seconds are about A billion seconds is about 32 years, almost half a lifetime

Seconds is about 32 years, almost a trillion seconds is about 32,000 years (the last ice age ended 12,000 years ago)

Much bigger and smaller

There are also prefixes for much larger and smaller numbers:

Some very large and very small numbers

Name The number prefix symbol

Very large ! Septillion 1,000,000,000,000,000,000,000,000 Yotta Y Sextillion 1,000,000,000,000,000,000,000 Zetta Z Quintillion 1,000,000,000,000,000 exa E Billiard 1,000,000 Small! quadrillionth 0.000 000 000 000 001 femto f quintillionth 0.000 000 000 000 000 001 atto a sextillionth 0.000 000 000 000 000 000 001 zepto z septillionth 0.000 000 000 000 010 0 000 0 010 0 000 0ytoytoy

All the big numbers we know

Name As a power of ten As a decimal thousand 103 1,000 million 106 1,000,000 billion 109 1,000,000,000 trillion 1012 1,000,000,000,000 quadrillion 1015 etc… Quintillion 1018

Sextillion 1021

Septillion 1024

Octillion 1027

Nonmillion 1030

Decillion 1033

Undecillion 1036

Duodecillion 1039

Trezillion 1042

Quattuor decillion 1045

Quindemillion 1048

Sexdemillion 1051

September Decillion 1054

Octodemillion 1057

November Decillion 1060

Vigintillion 1063 1 followed by 63 zeros!

And a googol is 1 followed by a hundred zeros (10100): 10,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000 Then there’s the Googolplex. It’s 1 followed by googol zeros. I can’t even write down the number because there isn’t enough matter in the universe to make up all the zeros: 10,000,000,000,000,000,000,000,000,000, … (Googol number of zeros) And a Googolplexian is one 1 followed by googolplex zeros. Wow.

All small numbers we know

Name As a power of 10 As a decimal Thousandths 10-3 0.001 Millionths 10-6 0.000 001 Billionths 10-9 0.000 000 001 Trillionths 10-12 etc … Quadrillionths 10-15 Quintillionths 10-18 Sextillionths 10-21 Septillionths 10- 24 Octillions 10- 27 Not millionths 10-30 decillionths 10-33 undepillions 10-36 duodecillionths 10-39 tredecillionths 10-42 quattuary decillionths 10-63

5627,5632,1927,1928,1929,1930,3473,3474,3475,3476

When I was in high school I read a book called Infinity: Beyond the Beyond the Beyond. I don’t remember much about it, but I’ll never forget the title. The concept of infinity in its… well, infinity… can haunt me for a long time. And the idea of ​​going “beyond the afterlife” – and then beyond! – provided more delicious food for thought. I think of that title and sensual infinity sometimes when I’m speaking at a school, as I was in West Chester, PA last week and someone asked, “What’s the largest number?” That’s a question I hear a lot . The conversation usually goes something like this:

Child: What is the largest number in the whole world?

David: Do you think there is such a thing as the largest number?

Target group: half “yes”, half “no”

David: Can someone please tell me what you think the largest number is?

Children, various: billions, trillions, quadrillions, quintillions, googol, googolplex, etc.

David: Wait a minute. Let’s say you think trillion is the largest number. What about “trillion-and-one” then? Isn’t that bigger? And if that’s the biggest, what about “trillion and two” – even bigger, right?

This usually leads to a triumphant retort over an enormous number familiar to many children (much less familiar to their parents and teachers):

Child: Googol must be the greatest!

David: What is a googol?

Many children know that “googol” is the name for a very large number – a one followed by a hundred zeros. It’s an exciting concept. In my book, G is for Googol: A Math Alphabet Book, I tell the story of how Googol got its name from a nine-year-old boy. Sure, it’s tempting to call Googol “the biggest hit,” but this is a non-starter.

Me: If you think googol is the largest number, what about googol-and-one? Or two googol? Or a googol googol?

Almost inevitably, at this point, someone will offer an even larger number, “googolplex.” It is true that the word “googolplex” was coined to mean a one followed by a googol zero. It’s way bigger than a flimsy Googol! Googolplex can describe the largest number with a single word, but of course that doesn’t make it the largest number. In a last ditch attempt to hold on to hope that there actually is such a thing as the greatest number…

Child: Infinity! Nothing is bigger than infinity!

True, but there is also nothing as big as infinity: infinity is not a number. It means infinity. A number denotes a specific amount.

So we finally agree: There is no such thing as the greatest number. But numbers as big as Googol or Googolplex continue to be enticing, and they should be. The most fascinating thing about Googol for me is how incredibly big it actually is. Writing those hundred zeros, while tedious, would only take a minute or two, but the amount represented is, as I said in G for Googol, “more than the number of hairs on the head of all the people in the world, more than the number of blades of grass on every lawn in the world, more than the number of grains of sand on every beach in the world – even more than the number of atoms in the universe.”

The estimated number of atoms is a one followed by 72 zeros (ten to the power of 72, but I can’t do exponents on this blog). Suppose the astrophysicists who estimated the number of atoms are way off the mark. Let’s imagine for the moment that the actual (albeit unrecognizable) number of atoms is a hundred times what is claimed. So it would be a one followed by 74 zeros – still way, way, way less than a googol.

The number “googol” is actually useless – except as food for a hungry mathematical mind. And it’s an especially nutritious numeric treat for young hungry minds. In fact, a kid with such a hungry young mind corrected me when I once said, “There’s no googol of anything anywhere.” The boy countered, “There’s more than one googol number. The number of numbers is infinite.” He was right! Now I change the statement: “There is no googol of any physical object.”

I’m less than enthusiastic about the point made by sixth graders in one class who sent me a stack of letters. All had the same basic theme, reflected in this one:

Dear Mr Schwartz,

How do you know how many hairs every person in the world has? You probably haven’t met every person in the world. Even if you did, babies are being born every minute. People lose hair every day!

No argument, but unfortunately this class didn’t seem to have a good understanding of the importance (and legitimacy) of the estimate.

Now, with the rise of a certain multi-billion dollar online company, it is necessary for me to include the following important disparity in any discussion of Googol, lest confusion arise:

It is interesting to note that the item on the right was the result of a spelling mistake. When Larry Page and his friends were choosing a name for a start-up company, he tried naming it “googol” after the huge number. Instead, he committed what is probably the most famous (and lucrative) misspelling in history. Regardless, there is absolutely no doubt that both “googol” and “google” are mighty big.

Right or wrong? Infinity is the number at the end of the real number line.

Why some people say it’s true: because infinity is the number greater than all other numbers.

Why some people say it’s wrong: because infinity isn’t a number and the number line has no end.

Reveal correct answer: \color{#20A900}{\text{Reveal correct answer:}} Reveal correct answer:

The statement is false \color{#D61F06}{\textbf{false}} false. Proof: The misconception at work here is that “as you keep going up the number line, past larger and larger counting numbers, eventually the counting numbers just give up (somewhere after the point your teacher gets tired of it has to make ticks). and there will be an infinity sign ( ∞ \infty ∞) there to mark the end of the number line.” Alternatively, some say that “Infinity is at the end of the number line, but there are still infinitely many numbers less than infinity and in between and every other point on the line.” Both terms have their roots in calculus-related concepts; however, they are both fundamentally wrong. When your teacher “ends the number line” with ∞ \infty ∞, it is actually a misleading shorthand for representing that the number line goes on forever. A less misleading way of presenting this notion might be to extend the number line with an arrow. We could additionally indicate that the integers continue after we have decided not to record them any more by we use the usual general notation for series: ” . . . n , n + 1 , n + 2 , . . . …n, n+ 1, n+2, … …n,n+1,n+2,…” to describe in this case the set of all non-negative integers. This set is also commonly known as “natural numbers ( N \mathbb{N} N)” or as “non-negative integers”. The misconception is to treat ∞ \infty ∞ as an integer or integer, or as one of the real numbers. The is not the same as believing that ∞ \infty ∞ is “real” or “unreal” in the English sense of the word. Infinity is a “real” and useful concept. However, infinity is not a member of the mathematically defined set of “real numbers ” and therefore not a number on the real number line. The set of real numbers, R \mathbb{R} R, is explained rather than defined in most pre-college schools. And even then, it’s usually explained only briefly, with a description the effect of “all points on a number line” and with the additional note that “the negative real numbers on the left of 0 and the positive numbers are those to the right of 0.” Most students are not taught a strict definition of real numbers unless they are majoring in mathematics at a university. One of the most common definitions to learn is that the real numbers are the set of Dedekind intersections of the rational numbers. For any rigorous definition of the real numbers, it is immediately apparent that “infinity” is not a member of the set of real numbers.

See general refutations: \color{#3D99F6}{\text{See general refutations:}} See general refutations:

Refutation: In the study of limits, infinity ( ∞ \infty ∞ ) is treated like any other number. Why do we do this in calculus when infinity isn’t actually a number? Answer: Many are taught about bounds in estimating or calculus exactly as you describe them, and the way infinity is treated misleadingly suggests that infinity is just another number. For example, given a function with a horizontal asymptote at 5, we could say that the limit of f ( x ) f(x) f(x) as x x x approaches infinity is five: f ( x ) x → ∞ = 5 f ( x)_{x\rightarrow \infty} = 5 f(x)x→∞​=5, and if f ( x ) f(x) f(x) has a vertical asymptote at 17 17 17, we get that taught we say that f ( x ) x → 17 = ∞ f(x)_{x\rightarrow 17} = \infty f(x)x→17​=∞. This is many students’ first encounter with ∞ \infty ∞, and it is a very misleading introduction as it implies that ∞ \infty ∞ can be treated as a number that is simply “greater than all other numbers”. In this context, however, infinity is just shorthand for a well-defined notion of a function that has no limit of real value but increases endlessly without limit. See the feature limits wiki for more details! Rebuttal: I’ve definitely seen infinity in math textbooks, and sometimes it’s defined as a number greater than all non-infinity numbers. Why is it there if it’s not a real mathematical concept? Answer: There are indeed mathematical sets of numbers, such as the cardinal numbers and the ordinal numbers, in which many differently defined versions of ∞ \infty ∞ are numbers. And strictly defined number systems containing ∞ \infty ∞ have many valuable applications. For example, in the set of cardinal numbers, infinity is a measure of how many real numbers there are. However, the set of real numbers R \mathbb{R} R is defined such that it omits any version of infinity. Furthermore, when considering the cardinal numbers, we must change our intuition about infinity: it is not a number in the “number line” sense, since the real numbers are applied. Instead, it’s a concept for measuring and comparing the sizes of sets.

False True True or False? ∞ is the number at the end of the real number line. \infty \text{ is the number at the end of the real number line.} ∞ is the number at the end of the real number line.

See also

A googol is 10 to the power of 100 (that’s 1 followed by 100 zeros). A googol is larger than the number of elementary particles in the universe, which is only 10 to the power of 80.

The term was coined by Milton Sirotta, the 9-year-old nephew of mathematician Edward Kasner, who asked his nephew what he thought such a large number should be called. Such a number, Milton apparently replied after a moment’s thought, could only be called something as stupid as “googol.”

Later, another mathematician came up with the term googolplex for 10 to the power of googol—that is, 1 followed by 10 to the power of 100 zeros. Frank Pilhofer has stated that given Moore’s Law (which states that a computer’s processing power doubles roughly every 1 to 2 years) it wouldn’t make sense to try to print a Googolplex for another 524 years – since all previous attempts Printing a Googolplex out would be overtaken by the faster processor.

Larry Page and Sergey Brin, the founders of Google, named their search engine after the term googol. In 1997, Larry brainstormed names with fellow Stanford students, including Sean Anderson, and looked at available domain names. Anderson mistyped googol as “google” and found it available. Larry liked it and the name “Google” stuck. Google’s corporate headquarters is called GooglePlex, an affectionately tongue-in-cheek reference to the origins of the company’s name.