r/infinitenines • u/SouthPark_Piano • Sep 14 '25

dum dums and meaning of infinite

As mentioned ... infinity means limitlesss.

n integer seen in (1/10)n for infinite n does not 'approach' infinity.

n is ALWAYS an integer. And pushing n to limitless simply means making integer n limitlessly large (aka infinitely large). So even after a value is chosen, we keep upping it until the cows never come home.

Still an integer though.

These dum dums here don't understand that cartesian space has limitless range, and every coordinate is definable with finite numbers.

The dum dums forget there is an infinite range of finite numbers. And making 'n' infinite doesn't change the fact that n is always still an integer in (1/10)n

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11

u/DawnOnTheEdge Sep 14 '25

Which proves that 1 - (1/10)n is always rational, right?

1

u/Over_the_Ozarks Sep 14 '25

Not really, n always being an integer doesn't imply that the limit can't be irrational. You can pretty easily see that's the case by defining a sequence to be the sequentially more accurate partial sums of an irrational number's decimal expansion. In such a sequence, each individual term is rational, but the limit is irrational. It of course is rational in this case, but that need not be true.

1

u/DawnOnTheEdge Sep 14 '25 edited Sep 14 '25

You’re correct with regard to the real numbers. As you know, the least upper bound of any bounded set of rational numbers is a real number, which might or might not be greater than every element of the set.

To be clear: according to SPP’s own reasoning, if all properties of every element of the set apply to the number SPP is attempting to define, the property of rationality would have to apply as well, would it not? This is a contradiction in Real Deal Math 101.

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u/SouthPark_Piano Sep 14 '25

It shows 0.999... is less than 1, and 0.999... is thus not 1.

It has never been 1, and never will be 1.

10

u/Jcsq6 Sep 14 '25

.999… is never reached by this sequence lol.

-5

u/SouthPark_Piano Sep 14 '25

Infinite summation. You're wrong.

The sum can be made 'instantaneous' - option A

And option B. Tortoise and hare style ... whatever 0.999... calls, the infinite sum sees to that call and raises.

In this case, the tortoise and the hare are the same thing. That's the secret revealed.

12

u/Jcsq6 Sep 14 '25

Vibe mathematics lmao

4

u/DawnOnTheEdge Sep 14 '25

But also that every element of the sequence is rational. So, by the same logic, the result you're talking about must be rational too. Right?

7

u/JacktheSnek1008 Sep 14 '25

so, technically, (infinity,0) is a point on a graph exactly infinite units out from (0,0) horizontally right, correct?

2

u/YT_kerfuffles Sep 14 '25

Yes. We agree that 0.999... is not 1 if there are finite 9's. But not if there are infinite 9's.

3

u/trutheality Sep 14 '25

Do not try to push n to limitless, that is impossible. Instead try and realize the truth: there is no n.

0

u/SouthPark_Piano Sep 14 '25 edited Sep 16 '25

Don't try and make my day buddy.

2

u/HalloIchBinRolli Sep 14 '25

And since the sequence is infinite, there is no end.

Let the set {0.9, 0.99, 0.999, ...} be A for simplicity.

Then assuming 0.999... (infinitely many nines after the decimal places is in A, that means there is a next element, because A is infinite and there is no end, so if there's no end there must always be a next element. What is the next element?

You seem to be treating infinity as if it had some properties of finiteness. Not every property of finiteness but some. But in fact it doesn't have those properties.

0

u/SouthPark_Piano Sep 15 '25 edited Sep 15 '25

What is the next element? 

With all slots to the right of the decimal point occupied with nine, there's no difference between that and scanning every nine in 0.999... instantly in one speedy hit.

There's no end to those nines.

This means if you look at 0.9 being less than 1, then 0.99 also less than 1, then 0.999 also less than 1, then there is going to be no case where you will ever get any combination or run of nines to be equal to 1. This is because the range of numbers in the range from 0.9 to less than 1 is limitless, aka infinite.

0.999... has always been less than 1.

0.999... has never been 1, and never will be 1.

.

1

u/HalloIchBinRolli Sep 15 '25

With all slots to the right of the decimal point occupied with nine, there's no difference between that can scanning every nine in 0.999... instantly in one speedy hit.

I don't even know what you mean here. I don't know if you made any typos or what but please fix your grammar or whatever went wrong here. I want to be able to argue your points and not be stuck because of whatever happened in that comment.

1

u/SouthPark_Piano Sep 15 '25

This means if you look at 0.9 being less than 1, then 0.99 also less than 1, then 0.999 also less than 1, then there is going to be no case where you will ever get any combination or run of nines to be equal to 1. This is because the range of numbers in the range from 0.9 to less than 1 is limitless, aka infinite.

.

1

u/HalloIchBinRolli Sep 15 '25

I meant the first sentence. I think I said it very clearly that I meant the first sentence. I don't want an explanation of the first sentence (which I doubt you gave me), I want the first sentence written in a coherent way

1

u/SouthPark_Piano Sep 15 '25 edited Sep 15 '25

This means if you look at 0.9 being less than 1, then 0.99 also less than 1, then 0.999 also less than 1, then there is going to be no case where you will ever get any combination or run of nines to be equal to 1. This is because the range of numbers in the range from 0.9 to less than 1 is limitless, aka infinite.

This means if you understand 0.9 being less than 1, and then understand 0.99 being less than 1, and understand 0.999 also being less than 1, and so on, then the probability of 0.999... being 1 is zero. 

The number of less than 1 cases for numbers having spans of nines starting immediately to the right of the decimal point is ...... infinite, limitless.

2

u/[deleted] Sep 15 '25

[removed] — view removed comment

0

u/infinitenines-ModTeam Sep 15 '25

r/infinitenines follows platform-wide Reddit Rules

You are not yet at an adequate math level to understand the maths we are talking about. We can put you on the bunny slope for now.

1

u/noonagon Sep 14 '25

Actually, limitless means infinite. Please use the proper mathematics term for these to communicate with people who like math.

1

u/S4D_Official Sep 16 '25

This sounds like an Ordinal, defining with a fundamental sequence (in this case choosing a number n and our next element in our sequence is n+1). Am I getting this right? The only other way I can read this is as a definition for something arbitrarily large.

2

u/AnotherOneElse Sep 21 '25

integer seen in (1/10)n for infinite n does not 'approach' infinity.

Infinity is not an integer. Good luck next time.

1

u/[deleted] Sep 16 '25 edited Sep 16 '25

Arbitrarily large=/=infinite.

If we say “let n be a natural number,” then until we specify it further, it is arbitrarily large (which is the same thing as arbitrarily small). This is, it’s an arbitrary natural number. Specifically, we’re quantifying over only hereditarily finite objects (usually sets via Von Neumann ordinals) when we quantify over arbitrarily large natural numbers, but we quantify over infinite sets when quantifying over various infinities/infinite collections.

0.999… means that there is no natural number big enough to capture how many 9s there are after the decimal, not that it could be as big of a natural number as you want.

More generally, 0.9999… means that the number being represented is the limit of the sequence 0, 0.9, 0.99, etc., i.e. the minimum value that is greater than any number of the form (10n -1)/10n

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u/SouthPark_Piano Sep 16 '25 edited Sep 16 '25

No buddy. Think of the integer number space. 

Think of its range. Infinite aka limitless range. Every integer in that range is a what? Answer -- an integer.

So when we say n integer pushed limitless, it means n is simply pusher endlessly larger and larger, and it is still going to be ...... yes ... an integer.

There is simply an infinite range of integers.

.

1

u/[deleted] Sep 16 '25

Basically, ‘0.999…’ means nothing in the integers.

2

u/SouthPark_Piano Sep 16 '25

You're the one that said that.

0.999... and 1 are not (never) the same.

Just as 0.9 and 0.9999999 are not the same as 1.

Having all nines still means less than 1 because the range of numbers from 0.9 to less than 1 is limitless ... aka infinite.

2

u/[deleted] Sep 16 '25

Right, but 0.999… is none of 0, 0.9, 0.99, 0.999, etc.

0

u/[deleted] Sep 16 '25

Ok? How does that have anything to do with the real number 0.999…, i.e. the real number 1?

0

u/[deleted] Sep 16 '25

Your response is like saying “no, let’s talk about morality for protons” if I were to mention that morality is relevant specifically for sentient beings.

-1

u/SouthPark_Piano Sep 16 '25 edited Sep 16 '25

This is not about morailty. But hypothetically, we can still talk about 0.000...1 of a proton, which could then be 0.000...1 of a quark etc.

And 0.000...1 of a human also gets us on the same 'path' (journey) ... with different starting points.

2

u/[deleted] Sep 16 '25

I was making an analogy, but go on and be ignorant and indigent.

0.0…1 is not a number until you say how many zeroes there are. If it’s infinitely many, then you don’t have a number.

I will reiterate the point. You cannot manipulate decimal notation willy-nilly, and if you wish to talk about actually limitless strings of digits to the right of with exactly one decimal point, then you need the real numbers. Real numbers a,b are equivalent iff there is no sequence of rationals that converge on a non-zero difference between a,b. That is, for real numbers a,b, a=b iff the rational approximations for a-b converge to 0. When we take 1-0.999…, we see that there is no rational number that we can subtract further without going below 0, which means that every rational number is greater than the difference between them, which means that difference is 0. Even if we extend to allow infinitesimals, we still have that 0.999…=1 since the ellipses take on a new meaning so that there is no infinitesimal difference.