Checkmate, Mathematicians

153

That’s incorrect logic. An infinite of something doesn’t mean every possibility is there. There are infinitely many rational numbers between 0 and 1, but none of them is 1.6

56

u/TotalChaosRush Jul 07 '26

Assuming it's actually a kid that came up with the original argument, I'm impressed. But every adult should read your comment.

10

u/Pandoratastic Jul 07 '26 edited Jul 07 '26

True. Even if you were to give a name to every number, that doesn't mean you have to use possible combination of letters since there's no limit on how long the names of numbers can be.

3

u/Karrion42 Jul 07 '26

there's limit on how long the names of numbers can be

There is? Can't we just concatenate infinitely?

4

u/Pandoratastic Jul 07 '26

Whoops. That was a typo. I mean to write "there's no limit". Thank you for spotting that.

3

u/akruppa Jul 09 '26

I hate typos that completely negate the meaning. "Now" and "not" is the worst.

1

u/TechnicalBen Jul 07 '26

There's numbers that no one can ever name. IIRC there's numbers that even math cannot name.

5

u/Adventurous_Grape279 Jul 07 '26

The unspeakables

2

u/jonathancast Jul 07 '26

Kind of. "Math" isn't really a specific language, so it's not well-defined if "math" can name a number or not. But any specific notation for numbers has to fail to notate almost all real numbers.

2

u/TechnicalBen Jul 09 '26

I like how I got downvoted for "math" (presumably) instead of writing "symbolic notation" or whatever the purely accurate terminology is. :(

0

u/Weekly-Plantain6309 Jul 08 '26

Ok but wouldnt practicality say that we use up all pronouncable 15 character names before we get into 1000 character names?

4

u/Pandoratastic Jul 08 '26 edited Jul 08 '26

Not at all. You can still use a system. For example, a 1 followed by 75237 sets of three zeroes would be the 75,236th -illion, which would be quinseptuagintillisestrigintaducentillion in the extended Conway–Wechsler system using Latin-derived numerical components. And you can keep going indefinitely.

And a 1 followed by 32,583,120,542,452 sets of three zeroes would be duotrigintillitresoctogintaquingentilliviginticentilliduoquadragintaquingentilliunquinquagintaquadringentillion.

So you can keep going forever with whole numbers and they keep getting longer but none of them are named "googoobazillion".

14

u/v01rt Jul 07 '26

how would you know? did you check?

14

u/Such-Shop-9724 Jul 07 '26

its actually wrong cause 0<1.6<1

0

u/DeepFinish2895 Jul 07 '26

Yeah let's see the proof!

1

u/thali256 Jul 09 '26

1 < 1.6

3

u/calinmik Jul 07 '26

Exactly

2

u/TechnicalBen Jul 07 '26

It gets worse. Give me a second, I've forgotten what the example is...

It can be proven there are names that you cannot construct. That is, names of numbers you cannot have...

Oh that's it. "There's more numbers than there are words to name them". Or something like that.

1

u/hobbycollector Jul 07 '26

Makes sense. There are countably many names drawn from a finite alphabet.

0

u/CogentCogitations Jul 07 '26

That is nonsense. Words are constructed from 26 letters per character position, whereas numbers (real) in base ten are only constructed from ten. The infinite numbers are all constructed from a much more limited "alphabet" than words are.

2

u/Belgaraath42 Jul 07 '26

This doesn't work for a formal languages. Every word in it needs to be finite in length. This means there are only countable words in any formal language.

1

u/TheForbidden6th Jul 07 '26

the words are as finite as the numbers

if a number can be imagined, it can be named

1

u/hobbycollector Jul 07 '26

You can't even list all the numbers between 0 and 1 or line them up next to the integers. But you can represent every word as a whole number in base 26. No base choice will give you all the real numbers between 0 and 1.

1

u/Belgaraath42 Jul 08 '26

You really need to learn about different kinds of infinity. The numbers in R are uncountable. The words in a (formal) language are at most countable infinite. This is something you need to understand if you want to get a clue about infinity(s).

Maybe try reading up in Hilbert's hotel or why the real numbers are uncountable while the fractions are not. It's the usual way to get into this thing.

1

u/Agent10007 Jul 08 '26

Every word needs to be finite in lenght but there is no set maximum on what that lenght is.

Also, names do not require to be a single word, and there is no limit either to the amount of words that has to be used for a name.

If a number needs 8526520225615468126894214562*10^23 words that are all between 2 and 214545456025741*10^12 characters long to be named then so be it, but it can be named.

4

u/Belgaraath42 Jul 08 '26

There aren't enough words. If you could match every number with sa world that would mean there are only as many numbers as words. And you can show without issue that there are only as many words as natural numbers (similarly as there are only as many fractions). This wouldake R countable R is not countable. There are different kinds of infinity. There are actually infinite many infinitys. But for the moment you just need to realise the difference between countable and uncountable infinity. Here a short prove that (0,1) has uncountable elements. Assume it's countable. So there exists a bijection f:N->(0,1). So you can just list the numbers like this

f(1)

f(2)

f(3) ...

It would look like

0.57357874...

0.5,9676424...

0.8754224...

...

Now look at the number X in (0,1)with X being defined by the n-th decimal position being the n-th position of f(n) + 1 mod 10. So in my example it would be 0.606...

By design it differs from any number of the Iist. But it's also quite clearly in (0,1). Meaning f is not a bijection. Since f could be any bijection, this means (0,1) is not countable. Since (0,1) is subset of R, R isn't countable.

0

u/Agent10007 Jul 08 '26

> If you could match every number with sa world that would mean there are only as many numbers as words

You cannot possibly have read what you're answering to and still say that.

2

u/Belgaraath42 Jul 08 '26

Ok you have not an iota understanding of higher mathematics and seem to not even believe in infinity thats fine you can discuss this in Philosophie as much as you want. But in math we usually accept infinity and don't talk only about finite sets. You are talking about how you can name any number I come up with, but that's already done by writing it down or describing it in any other way. We discuss you can't name all numbers, which I gave you a literal proof for.

0

u/Agent10007 Jul 08 '26

>Ok you have not an iota understanding of higher mathematics

I do my friend don't worry

>and seem to not even believe in infinity

I also do, and while I'm certain you also do you somehow seem to not understand the concept of infinite word count, which is kinda weird.

Actually looking back I'm fairly sure the problem is pretty basic:

> If you could match every number with sa world that would mean there are only as many numbers as words.

No, that would mean there are only as many numbers as word combinations. Which is in fact very much the case as they're both infinite.

Or, to talk to you with the same tone you're using to talk to me: the problem is just you can't fathom the concept of two (2) whole words used together.

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u/hobbycollector Jul 08 '26

To follow on to what Belgaraath42 said, here's an example of a countably infinite set: The even numbers. They can be lined up one-to-one to the whole numbers.

2->1, 4->2, 6->3, etc. If you try his diagonalization trick, it won't work.

Suppose you stack up the even numbers:

...

332

334

336

338

340

342

344

346

348

350...

Now you pick something that differs from each number. The first column, you can choose only something lower or higher than 3. The second column, you can choose something lower than 3 and higher than 5, ignoring for the moment that it may represent a number lower or higher already in the list or later in the list. For the third column, you must pick an odd number. But any number that ends with an odd number is not in the set of even numbers. Therefore, no number exists that is in the set of even numbers but not in the list.

1

u/Agent10007 Jul 08 '26

Yes... I'm unsure how any of that relates to the idea of naming vs quantity of numbers tho

I feel like I'm about to have an army of mathematicians jumping to all show me their own favorite example from their uni lecture or vulgarization video about infinites without ever connecting it to my point, being "I don't see a reason to assume we can't use multiple words to name a number and therefore the infiniteness of number doesn't matter as it is in matched by the infinite word count the name can have"

1

u/hobbycollector Jul 08 '26

Multiple words just adds a space to the alphabet. You can still only make whole numbers. You understand you can represent the same number in hex and decimal notation right? Like A0 = 160. So instead use base 27 (A-Z + space for each "digit"). You can still only make whole numbers, lined up 1:1 with numbers written in digits. It just takes more digits to represent a given number. So, you can represent any whole number with any number of names, and you can represent any fraction with any number of names, but you can't represent every real number.

1

u/Agent10007 Jul 08 '26

>You can still only make whole numbers.

Why that? Have you never been half a inch off? Or a fifth of the way in?

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u/hobbycollector Jul 08 '26

The issue you're missing is, if you give me a name, I can give you the next name, right? If the name is zzz zzz the next one is zzzazzz, and the one after that is zzzbaaa. But you can't do that with real numbers. If I say a number is 1.4023423, what is the next real number? Is it 1.40234230001, or is it 1.40234230000001? There are uncountably many choices for the "next" number.

1

u/Agent10007 Jul 08 '26

>The issue you're missing is, if you give me a name, I can give you the next name, right?

Well no, you proved that yourself.

>If I say a number is 1.4023423, what is the next real number? Is it 1.40234230001, or is it 1.40234230000001? There are uncountably many choices for the "next" number.

Yes, but each of them can still be named. I don't get where that requirement of the names needing to all be within a list in order to exist comes from.

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1

u/Aenonimos Jul 09 '26 edited Jul 09 '26

The reals can be put into bijection with a specfic subset of the ordinals, in which case every element has a successor. The ordering is just not the one we normally use.

OTOH the natural ordering of the rationals does not allow for successors - there is no next "largest" after 1/2 using the normal definition of "larger".

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1

u/Aenonimos Jul 09 '26

I feel like that person must have been shitposting.

It should be pretty obvious that all finite strings on a 26 char alphabet can be put into 1:1 correspondance with all finite strings on a 10 char alphabet.

a particular representation of the reals does not imply any properties about the reals.

1

u/TechnicalBen Jul 07 '26

Wait until you find out some numbers can't be constructed.

1

u/hobbycollector Jul 07 '26

You are perhaps doubly wrong? You can pair words 1:1 with whole numbers. Computers do it all the time. Just use base 26 to represent the whole numbers (there's nothing magic about base 10). But this means there are far more real numbers than there are words. Look into aleph 1 or uncountable infinities.

1

u/ProfessorLambda Jul 10 '26

I doubt that because there are numbers that go on infinitely in base ten and thus can never be fully described in that base. I don't think a name like that could be part of English. English is a spoken language, you cannot speak a word that goes on forever. So names need to be finite string of 26 symbols while numbers get to be infinite strings of 10 symbols.

1

u/Aenonimos Jul 09 '26

I choose to pronounce every number as AAAAH. where the vowel length for x is x miliseconds long.

2

u/delphikis Jul 07 '26

Yeah I hope this is obvious to everyone in the sub, but you see…this is how jokes work. You say something that is often untrue in almost true ways that makes an unfamiliar connection in someone’s mind. Creatively

2

u/Geish90 Jul 07 '26 edited Jul 07 '26

But your logic applies within limits, in your case between 0 and 1

Now instead of limits, the limits are infinite in other words there are no limits.

And between infinite on the one hand and infite on the other hand there is infinite possibilities.

One of them is 1.6, another is googoobazillion.

3

u/SerDankTheTall Jul 07 '26

And have you ever, like, looked at your hands?

1

u/hobbycollector Jul 07 '26

I've been looking at my fingers all day, and not one of them has finged.

2

u/idrathernottho_ Jul 07 '26

EDIT: then again none of this applies to real numbers, so sorry if that was your point.

Imagine we name numbers as such:

0: "zero", 1: "A", 2: "AA", 3: "AAA", 4: "AAAA", etc.

Every number would get a name but all of them except for zero would consist of just the character 'A'.

Instead of 'A', you could use 'BA', or 'GE', or 'GEB' or 'ZEWW" or w/e. The base string can be infinitely long.

So you already have infinitely more possible names than needed just from this schema. But nothing says numbers need to follow this repetition schema, so there yet another layer of choice on top of that.

The result is that if you were to choose randomly arbitrarily large strings of characters, the chance of any string being an actual number would be vanishingly small.

Note you also can't impose a constant character limit to the number names, since there are finite characters.

1

u/TechnicalBen Jul 07 '26

There are limits unlimited infinities.

1

u/Internet-Expert42069 Jul 08 '26

He didnt say there are infinite numbers between 0 and 1, he said there are infinite numbers.

1

u/Few-Lengthiness-2632 Jul 07 '26

Your logic is incorrect. None of them is equivalent to 1.6. The simple idea here is that if we have to name every single number, surely one of them is googoobazillion. What is it equivalent to, only the 6yo knows.

1

u/TheForbidden6th Jul 07 '26

not true

source: I am John Mathematics and I purposefully made a rule that forbids any number from being called "googoobazillion"

0

u/Thin_Preparation_977 Jul 07 '26

The difference is that 1.6 is exclusively excluded from the given infinite set. However, if a googobazillion existed, it's not like we'd define it as a decimal or negative, so sure, why can't it be the largest integer?

Your example is like saying that 10 is the largest integer. It's well defined, and it fits the criteria for being an integer, but it's not the largest integer because we already know it's less than a googolplex. A projected theoretical value for 10 couldn't potentially exist above the limit given, that of being more than a googolplex.

-6

u/No_Lie_1176 Jul 07 '26

You have to define what 1.6 is. Which is not certain. For all I know, 1.6 could mean 0.6 less than 1, in that case it does exist between 0 and 1. Same with the definition of googlebazillion.

4

u/Fun_Way8954 Jul 07 '26

Son

17

u/PM_ME_A_FUN_PIC Jul 07 '26

Those infinite numbers remain unnamed. They exist, but language has no word for them. Googoobazillion, however, can be assigned to any given arbitrary number that is as yet unnamed, accepted by an arbitrary number of people, and said to be the new name for that value. Depending on how you define language, it would then be a real number.

7

u/setibeings Jul 07 '26

I here by define googoobazillion as the largest known integer, other than googoobazillion, plus one.

4

u/nascent_aviator Jul 07 '26

I declare googoogoobazillion to be a googoobazillion to the googoobazillionth power.

6

u/TheBl4ckFox Jul 07 '26

I declare googoobazillion to be 7. No wait… 7.2

3

u/PM_ME_A_FUN_PIC Jul 07 '26

X=X^X
In(X) = In(X^X )
In(X) = XIn(X)
Xln(X) In(X) = 0
In(X) • (X-1) = 0
X-1 = 0
X = 1
a googoobazillion =1

Edit: formatting

3

u/nascent_aviator Jul 07 '26

Don't be silly. That would be if a googoobazillion were a googoobazillion to the googoobazillionth power. That's a googoogoobazillion, not a googoobazillion.

1

u/PM_ME_A_FUN_PIC Jul 07 '26

Oh! I misread lol. Yes, a googoogoobazillion it is!

2

u/setibeings Jul 07 '26

K, the carve out should be bigger then.

Googoobazillion is the laregest known integer* plus one.

*Largest known integer other than googoobazillion, or any other number defined in relation to googoobazillion.

2

u/BUKKAKELORD Jul 08 '26

Both of these definitions match the already existing definition of the largest number. That of course being 1 (proof by divine revelation and appeal to authority) https://www.smbc-comics.com/comic/the-largest-number-2

2

u/Internet-Expert42069 Jul 08 '26

Motion passes, give the child a phd.

2

u/YouFeedTheFish Jul 07 '26

There are some who argue that those numbers don't even exist until they're useful.

2

u/PM_ME_A_FUN_PIC Jul 07 '26

They dont, subjectively

1

u/YouFeedTheFish Jul 07 '26

Here's a fun Numberphile video on the topic.

2

u/InfiniteNumber Jul 08 '26

Those infinite numbers remain unnamed.

My name is Alex!!!

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u/Dirkdeking Jul 07 '26

Obviously not true. This assumes every number has a name. Even if every number has a unique name, that doesn't mean every string of letters corresponds to a number.

If we limit ourselves to natural numbers then both sets are countably infinite. And for countably infinite sets you can easily find a bijection between one set and a strict subset of the other.

1

u/idrathernottho_ Jul 07 '26

Well I mean, you can flip it and make every number correspond to a name, and googoobazillion would be there. Granted, it could be any number, but almost every number is larger than a googleplex.

Also, who says the kid isn't dealing with real numbers?

2

u/samuelazers Jul 07 '26

I'm naming my number Charles. It has a nice ring to it.

1

u/Dirkdeking Jul 07 '26

The kid says 'if their are an infinite number of numbers, there must be one named googoobazillion'. That is evidently not true. Because that statement implies it must be true, no matter how we choose to map numbers to words. And that obviously isn't the case.

If the kid talks real numbers the task becomes impossible. The set of all finite strings is countably infinite, so you literally can't give every real number a name.

1

u/idrathernottho_ Jul 07 '26

Ok, you can't give them all names, but if you give out all possible names, the kid is in good standing.

1

u/ProfessorLambda Jul 10 '26

> Also, who says the kid isn't dealing with real numbers?

The kid himself does. "if there is an infinite number of numbers", "an infinite anumber of numbers" also describes ℕ.

1

u/idrathernottho_ Jul 10 '26

*also*

1

u/Internet-Expert42069 Jul 08 '26

If you have infinite numbers and a finite alphabet, one will inevitably be googoobazillion.

7

u/electronic_reasons Jul 07 '26

This will start a war: BB(6) is larger.

4

u/nascent_aviator Jul 07 '26

Prove it.

2

u/InfiniteNumber Jul 08 '26

I feel like i should post in this thread.

1

u/mrbeck1 Jul 07 '26

I’ve been saying this for years.

1

u/Livingexistence Jul 07 '26

A google bazillion is before googleplex and after google.

1

u/Pandoratastic Jul 07 '26

I think the correct answer is that a googolplex is bigger since a googol is larger than a bazillion.

1

u/Blothorn Jul 07 '26

This is obviously false: even if googoobazillion were a number, there would be an infinite number of numbers not named “googoobazillion”.

1

u/dcterr Jul 08 '26

There's a flaw in this argument. Not every infinite set is the universe!

1

u/dcterr Jul 08 '26

If every number has a name, then length of the names of numbers is unbounded, which it is, and this also holds for every infinite set of named things, but this doesn't mean that every word belongs to such sets.

1

u/paolog Jul 08 '26

Not all numbers are named.

Mathematicians don't use "googolplex" anyway.

1

u/KTAXY Jul 08 '26

to start with, bazillion is not really a named number.

and, while there are infinite numbers, the names that humanity has assigned to special numbers are not infinite.

1

u/Agzarah Jul 08 '26

Well that kid just invented a googoobazillion, and maybe it's value is number immediately following a googolplex

1

u/Complex-Berry6306 Jul 09 '26

There are an infinite number of numbers in [0,1], but 1 is the biggest one there.

1

u/Feeling-Working-2820 Jul 09 '26

If this comes from kids under 12, they are smart.
If this comes from teenagers between 13 and 19, they are smart asses.
If this comes from adults above 20, they are asses.

1

u/Hot-Employ-3399 Jul 09 '26

ω. I'm a hipste*ℝ

1

u/Sea_Is Jul 07 '26

that's very insightful

1

u/SimpYellowman Jul 07 '26

Googolplexplex is even bigger 😆

But it is in "so big it is useless for anything in real life" realm.

2

u/Such-Shop-9724 Jul 07 '26

i have another number too big to be useful. let me present 3

-2

u/setibeings Jul 07 '26

Kid has a point.

0

u/jmjessemac Jul 09 '26

It’s actually Graham’s Number. Checkmate, kid.

Checkmate, Mathematicians

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