What Is The Biggest Infinity

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My son's in first grade now, which I still don't quite believe. But it's true. And, thanks to first grade, he's really starting to get a handle on this ususual technology we call 'math'. It's just adding and subtracting right now, but he's really getting excited about it. He'll ask me random math questions, and ask me what my favorite number is, and so on and so forth. Then, one day, he asks me this: 'What's the biggest number?'

Well. I'm ready for this. One of the classes I took for my woefully under-used BS in Computer Science and History was on logic and number theory. 'There isn't one.'

So at last we have finally found a larger infinity than ℵ 0! Perhaps not surprisingly, this new infinity—the cardinality of the set of real numbers ℝ—is called ℵ 1. It's the second transfinite cardinal number, and our first example of a bigger infinity than the ℵ 0 infinity we know and love. Infinity isn't a number, it's a concept. The idea is that there is no 'biggest number in existence,' because the number line just goes on and on. You could say googol, which has 100 zeros (yes.

'Yes there is!' he declares.

  1. There is no biggest, last number except infinity. Except infinity isn't a number. But some infinities are literally bigger than others. Let's visit some of them and count past them. Video source: Vsauce /.
  2. There is no largest number under infinity because what ever the highest number is, one can always be added to it, making the new number the highest number. What is under statue of liberty's robe.
  3. Is the largest number infinity? A googol is a 1 with a hundred zeroes behind it. We can write a googol using exponents by saying a googol is 10^100. The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100). That's written as a one followed by googol zeroes.

'No,' I tell him. 'Because, no matter what, you can always add one to the number.'

'No you can't!' he insists, shocked by his first glimpse of the concept of infinity.

'Well,' I ask him, 'what's the biggest number you can think of?'

'A googol!' he announces with some confidence.

'Do you know what that is?' I respond. His puzzled expression tells me he doesn't, so I fill him in. 'You know how one hundred is one followed by two zeros, right?' He nods. 'Well, a googol is one followed by a hundred zeros.'

His eyes go wide. 'What's a googol take away one?' he asks.

'That would be…' I think for a moment. 'Ninety-nine nines.'

'Wow,' he says. 'What's that called?'

'Uhm… I don't know.'

What is the biggest number?

Like I said, there really isn't one. You can always add one to any arbitrarily large number. A googol, for example, is one followed by a hundred zeros. It looks like this (adjust your browsers, please):

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

Pretty big, right? Well, a googol plus one is:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,001

Clearly, all of these zeros get unwieldy in an absurdly short period of time. That's why exponential notation is used. This, if you're not familiar with it, is written in the format xy and means that x is multiplied by itself y times. 32 is 3*3 (equaling 9), while 23 is 2*2*2 (equaling 8). For convenience, since we count by 10s, most numbers are presented in a 10y format – sometimes called 'scientific notation'. In this format, a googol is 10100, which you'll have to admit is a whole lot easier to write than all those zeros I typed out above.

We do have names for a lot of really big numbers, though. Oddly enough, the names you use depend on whether or not you are using the 'long scale' of numbering, the 'short scale' of numbering, or Metric prefixes.

Hang on. I know what Metric is, but what's short scale and long scale?

Brace yourself. The rabbit hole goes deep, here.

Short and long scale is just different ways of naming really big numbers, depending on where you live. According to Wikipedia, most English-speaking and Arabic-speaking countries use short scale, while most other countries in continental Europe and most countries that speak Romance languages use long scale. The difference sounds simple, and is all based on what you call numbers bigger than a million (106). Here goes:

  • When using short count for numbers larger than a million, you get a new name every time you get 1,000 times larger. So you count 1 million, 10 million, 100 million, 1 billion.
  • When using long count for numbers larger than a million, you get a new name every time you get 1,000,000 times larger. So you count 1 million, 10 million, 100, million, 1,000 million, 10,000 million, 100,000 million, 1 billion.

Simple, right?

No.

Yeah, it kind of confused me too. I grew up using short count, so it looks intuitive and long count looks really wierd. I'm sure that if I grew up counting long count instead, than I'd flip those attitudes. Maybe a table would help? How do i play roulette.

Probably

All right. Here goes. Brace yourself.

NumberShort CountLong CountMetric Prefix
1OneOneN/A
10TenTendeca-
102HundredHundredhecto-
103ThousandThousandkilo-
106MillionMillionmega-
109BillionThousand Million (or Milliard)giga-
1012TrillionBilliontera-
1015QuadrillionThousand Billion (or Billiard)peta-
1018QuintillionTrillionexa-
1021SextillionThousand Trillion (or Trilliard)zetta-
1024SeptillionQuadrillionyotta-
1027OctillionThousand quadrillion (or Quadrilliard)N/A
1030NonillionQuintillionN/A
1033DecillionThousand quintillionN/A
1036UndecillionSextillionN/A
1039DuodecillionThousand sextillionN/A
1042TredecillionSeptillionN/A
1045QuattudorcellionThousand septillionN/A
1048QuindecillionOctillionN/A
1051SexdecillionThousand octillionN/A
1054SeptendecillionNonillionN/A
1057OctodecillionThousand nonillionN/A
1060NovomdecillionDecillionN/A
1063VigintillionThousand decillionN/A
1066N/AUndecillionN/A
1069N/AThousand undecillionN/A
1072N/ADuodecillionN/A
1075N/AThousand duodecillionN/A
1078N/ATredecillionN/A
1081N/AThousand tredecillionN/A
1084N/AQuattuordecillionN/A
1087N/AThousand quattuordecillionN/A
1090N/AQuindecillionN/A
1093N/AThousand quindecillionN/A
1096N/ASexdecillionN/A
1099N/AThousand sexdecillionN/A
10100GoogolGoogolN/A
10102N/ASeptendecillionN/A
10108N/AOctodecillionN/A
10114N/ANovemdecillionN/A
10120N/AVigintillionN/A
10303CentillionN/AN/A
10600N/ACentillionN/A
1010100GoogolplexGoogolplexN/A

There are, of course, proposals for names for larger numbers. I won't go into too many details here, beyond saying that the proposed name for the number 103003 is 'millinillion' for short count naming conventions and 'thousand quingentillion' for long count naming conventions. And now you know.

But, what about infinity? Isn't that the largest number?

Nope.

What? But, I've always heard…

'Infinity' isn't the largest number, because infinity isn't a number. Infinity is a concept, and in numbers it refers to either an arbitrarily large or undefined number (such as how the value of X/0 goes to infinity in calculus), or it represents sets of numbers. When using infinity as a set, you get two basic types of infinity: countable, and uncountable. Countable infinity is an infinite set whose 'elements can be put in one-to-one correspondence with the set of natural numbers. In other words, one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time.' Basically, it's a clearly defined set. All natural numbers (1, 2, 3, 4, … infinity) is a countable infinity. So is all even numbers, all odd numbers, all prime numbers, and so forth.

Uncountable infinities, on the other hand, aren't quite so neat. An uncountable set 'contains so many elements that they cannot be put in one-to-one correspondence with the set of natural numbers. In other words, there is no way that one can count off all elements in the set in such a way that, even though the counting will take forever, you will get to any particular element in a finite amount of time.' For example, the set of all real numbers between 0 and 1 is uncountable. Why? Because there will always be an infinite number of fractions between any two members of that set you care to name.

Could you try and make all that a little clearer?

Sure. A countable infinity has a finite (although possibly large) number of points between any two elements of the set. An uncountable infinity has an infinite number of points between any two elements of the set. As an example, take the countable set of all natural numbers. If you pick a starting point (let's say the number 12) and an ending point (let's say the number 17), then it you have to count only 5 steps to get from 12 to 17. If your starting and ending points were 2 and a googol, then you'd have to count 9,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,999,998 steps – that's a whole lot of counting, but you could do it in a finite (but large) amount of time. It can be counted.

Now, consider the set of all real numbers between 3 and 5. It looks shorter at first glance, but remember that real numbers include fractions and decimals. So, let's pick our starting point as 3.0001 and 3.0001001. 3.00010001 is between them. So is 3.00010002, and 3.00100000000007, and every other amount of extra decimal places that could conceivably be tacked on. And since there is no limit to the number of extra decimal places, you would never be able to count every single possible number that lie between 3.0001 and 3.0001001. Ever. It cannot be counted, so it is uncountable.

My head hurts.

Mine, too. Now, let me make it hurt worse. Uncountable infinities are larger than countable infinities, even though both infinities are infinite in size.

What?

Biggest

Yes, and it's all down to that the countable versus uncountable aspects of the sets. Let's look at the set of all natural numbers versus all real numbers, and then count the 'steps' between 2 and 3. The countable infinite has a finite distance between those two numbers, while the uncountable infinity has an infinite distance between the two numbers. So the uncountable infinity is larger because, between any two arbitrary points, it is larger than the countable infinity for the same segment of the set.

So, in summary, there is no 'largest number'. You can always add one to any number you choose (a millinillion and one, a millinillion and two, a millinillion and three,…), and infinity doesn't count because it's not a number. Even when it's countable. And a googol take away one would be called, in short count, 'a googol minus one' because I couldn't find a short count name for numbers that big.

A googol is a 1 with a hundred zeroes behind it.

We can write a googol using exponents by saying a googol is 10^100.

Biggest Number That Isn't Infinity

The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100).

That's written as a one followed by googol zeroes.

What is the biggest number in the world besides infinity?

The largest number that has a commonly-known specific name is a 'googleplex', which is a 1 followed by a googol zeros, where a 'googol' is (a 1 followed by 100 zeros).

Is a googolplex number bigger than infinity?

Almost inevitably, at this point someone proffers an even bigger number, 'googolplex.' It is true that the word 'googolplex' was coined to mean a one followed by a googol zeros. It's way bigger than a measly googol! True enough, but there is nothing as large as infinity either: infinity is not a number.

What is the last number before infinity?

One was called 'psi', and it was supposed to be the 'last' finite number, i.e., the number just before infinity. The second was called the 'end number', which is supposed to be the highest in the kingdom of numbers. Nothing is larger than the end number because by definition it is the last number.

What is the name of the highest number?

Numbers Bigger Than a Trillion

NameNumber of ZerosGroups of 3 Zeros
Octodecillion5719
Novemdecillion6020
Vigintillion6321
Centillion303101

22 more rows

Do numbers ever end?

The sequence of natural numbers never ends, and is infinite. There's no reason why the 3s should ever stop: they repeat infinitely. So, when we see a number like '0.999' (i.e. a decimal number with an infinite series of 9s), there is no end to the number of 9s.

What's the smallest number in the world?

The smallest version of infinity is aleph 0 (or aleph zero) which is equal to the sum of all the integers. Aleph 1 is 2 to the power of aleph 0. There is no mathematical concept of the largest infinite number.

What Is The Largest Infinity Suv

Can we understand infinity?

For many of us, it's easy to understand the concept of infinity, but we can't comprehend how 'big' or 'never-ending' it is, because our perception of time always has a beginning and an end — minutes, days, years, lifespans.

What is the smallest number?

What Is Bigger Than Infinity

The concept of infinity in mathematics allows for different types of infinity. The smallest version of infinity is aleph 0 (or aleph zero) which is equal to the sum of all the integers. Aleph 1 is 2 to the power of aleph 0. Play on line casino. There is no mathematical concept of the largest infinite number. Gambling in vegas for beginners.

Is infinity a real number?

Infinity (symbol: ∞) is a concept describing something without any bound, or something larger than any natural number.

Do numbers end Yes or no?

No, there is no end to the counting numbers 1, 2, 3, and so on. It can't be the biggest number because you can just add 1 to 11 and get a bigger number, namely 12. And so on, and so forth. The general idea is that for any given number, it's always got a bigger neighbor.

What's the number of infinity?

The other type of infinity is uncountable, which means there are so many you can't ‘number' them. An example of something that is uncountably infinite would be all the real numbers (including numbers like 2.34. and the square root of 2, as well as all the integers and rational numbers).

Can Infinity have a beginning?

It really just depends on the infinity you describe, whether it will have a beginning or not. Most infinities do have beginnings, simply because in order to tangibly grasp the concept of whatever infinity we are talking about (just based on the limitations of the human mind) we generally need a starting point.

Is a zillion a real number?

A zillion is a huge but nonspecific number. Zillion sounds like an actual number because of its similarity to billion, million, and trillion, and it is modeled on these real numerical values. However, like its cousin jillion, zillion is an informal way to talk about a number that's enormous but indefinite.

What is a Googolplexianth?

A googolplexianth is the biggest amount of whatever at least, the one that has been given an official name, yet is bigger than Infinity.

What is higher than a trillion?

After a billion, of course, is trillion. Then comes quadrillion, quintrillion, sextillion, septillion, octillion, nonillion, and decillion.

Is Infinity equal to infinity?

One ‘value' of infinity could be different to another, or it could be the same – basically, the word infinity is so ambiguous that we can't say for sure that infinity equals infinity. Also, according to google, infinity is anything greater than numbers.

Is infinity minus 1 still infinity?

Infinity is not a number is a concept, but let's imagine one infinity made out of numbers from 0 to infinity: You will have th following list: 0, 1, 2 ,3followed by a never ending list of numbers. So in this case, this infinity minus one is still infinity.

Whats the highest number someone has counted to?

That's right—the highest number a single human has ever counted to is a nice, even one million. Harper still holds the record for the highest number counted out loud by one person. According to todayifoundout.com, he counted for about 16 hours every day, without taking a day off, leaving his apartment, or even shaving.

Which is the biggest shark in the world?

O. megalodon

What comes after decillion?

Higher still, quintillion is used to refer to the mass of the earth (in tons) and the number of molecules in the human brain. Those numbers, in ascending order, are sextillion, septillion, octillion, nonillion, and decillion.

Will Pi ever be solved?

Technically no, though no one has ever been able to find a true end to the number. It's actually considered an 'irrational' number, because it keeps going in a way that we can't quite calculate. Pi dates back to 250 BCE by a Greek mathematician Archimedes, who used polygons to determine the circumference.

Is Infinity and one a number?

The first is that infinity is the largest number there is. The second is that adding one to any number gives you an even larger number. There is also a strong intuition we have that says infinity ought to equal infinity plus one.

Why is the infinity symbol a sideways 8?

The shape of a sideways figure eight has a long pedigree; for instance, it appears in the cross of Saint Boniface, wrapped around the bars of a Latin cross. However, John Wallis is credited with introducing the infinity symbol with its mathematical meaning in 1655, in his De sectionibus conicis.

Is Infinity an even number?

Infinity is an adjective used to describe any number whose magnitude is larger than that of all finite numbers. There exists infinite numbers that are odd, infinite numbers which are even, and infinite numbers which are not integers, and these latter values are not even and not odd.

What's more than infinity?

What Is The Largest Infiniti Car

With this definition, there is nothing (meaning: no real numbers) larger than infinity. There is another way to look at this question. It come from an idea of Georg Cantor who lived from 1845 to 1918. Cantor looked at comparing the size of two sets, that is two collections of things.

Can the past be infinite?

What Is The Largest Infinity

Since there's no negative infinite number, there's no infinitely past year or earliest year. There never was a time when the past became infinite because no set can become infinite by adding any finite number of members. So, if the past is infinite, then it has always been infinite.

How many zeros are there in infinity?

Photo in the article by 'Wikipedia' https://en.wikipedia.org/wiki/Natural_satellite

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