r/infinitenines

The 0.999... you talk about is not the actual 0.999... we talk about. Your 0.999... terminates, as implied by your statement from a recent post:

>where the pre-requisite number of nines that begins to qualify 0.999...9 is the largest number you can or cannot generate with your brain

The actual 0.999... is non-terminating - that means it has infinite amount of nines after the decimal point, not just "the largest number you can think of".

It never, at any point in time, has a finite number of nines. Example:

Let's say someone's brain can only generate a number that's no more than 10^1000. Does that start to qualify as 0.999...? No, it does not, because the number 10^1000 is finite.

Let's say someone's brain can only generate a number that's no more than 10^(10^1000). Does that start to qualify as 0.999...? No, it does not, because the number 10^(10^1000) is finite.

I hope you see the pattern.

Doesn't matter which integer you plug in as n , since an integer that would give you the actual 0.999... doesn't exist.

Note that it is very important to understand that infinity is not an integer. Remeber that bud.

Also, you correctly say that 0.999... = 0.9 + 0.09 + 0.009 ..., yet you incorrectly conclude that it does not equal to 1.

As you don't seem to know, an infinite summation is equal to the limit of the sequence of it's partial sums, but there is no point in teaching you this because you don't even understand limits.

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I'm curious about y'all's opinions on this - is the 0.999... SPP (and maybe some others) talks about the same as the 0.999... we talk about?

Edit: Sorry for the broken formatting.

And for the ones you don't agree with, would you agree that they are equal to 1?

1. The number with the property that for all natural n ≠ 0, the nth digit past the decimal point is 9
2. lim x →∞ 1 - 10^x
3. lim x →∞ sum from n= to x (9/10^n)
4. 1/3 * 3 = 0.333... * 3 = 0.999...

Edit: Fixed 3

And if you believe that the pattern breaks somewhere, why do you believe that?

You're goal is to make line between 2 points, point A and point B, and you make a line halfway from point A to point B and then make a line halfway from the end of the last line you made and to point B. Continue this forever and what happens? You should not be able to make a line from point A to point B because you can never close the gap because you are only going to close it halfway. But you keep adding numbers infinity between the distance and adding numbers infinity times

(x*infinity=infinity

X is not equal to 0)

So does that mean every gap that is more than 0 units is infinite?

PLEASE QUESTION MY LOGIC I KNOW I AM WRONG I WANT TO KNOW HOW I MESSED UP SONEWHERE

No real number fit between 0.999...8 and 0.999...9 too, so they are equal

No real number fit between 0.999...7 and 0.999...8 too, so they are equal

After some induction, we find that no real number fit between 0.000...0 and 0.000...1 too. 0=1 QED

Locked immediately because not a genuine question, but here's an answer:

https://preview.redd.it/yjple23f570h1.png?width=1310&format=png&auto=webp&s=981ead13c89125625a54ecd7192729021638075a

Can you please do the same for sqrt(0.999...)?

And before you flip out over not writing down digits, recall that a number is not the same thing as its representation. The number 1/2 can be expressed in many ways, but the number is an abstract concept. We don't care about decimal representations other than being able to express in a convenient but by no means unique way a number. Decimal representations aren't a number. They're a way to write down a number to convey the abstract notion from author's brain to reader's brain.

So an infinite series is how pi is defined. The integral above is one way to express the square-root of pi. And I usual express answers that involve root-pi in terms of root-pi. For example the probability density function of a normal random variable. Or, if z~N(0, sigma) then E(|z|)=sigma*sqrt(2/pi). I don't write sigma*sqrt(2/3.14159....) because I'm not an animal.

But back to the question: What is a the square root of 0.999...?

Don't engage in embarrassing "I know you are, but what am I" arguments. I gave you an expression for root-pi other than root-pi. Can you do the same?

Edit: typo.

In Analysis I by Terence Tao, Tao rigorously develops the real number system and proves basic results of real anlysis. In Appendix B, he formally defines the decimal system. Proposition B.2.3 in particular reads:

>Proposition B.2.3 (Failure of uniqueness of decimal representations). The number 1 has two different decimal representations: 1.000... and 0.999....

>Proof. The representation 1 = 1.000... is clear. Now let’s compute 0.999.... By definition, this is the limit of the Cauchy sequence

>0.9, 0.99, 0.999, 0.9999, ... .

>But this sequence has 1 as a formal limit by Proposition 5.2.8.

Now that this rookie mistake by Terence Tao has finally been exposed, should I throw this textbook in the trash?

Like, if you are given the information that x=y and y=z, do you believe you can conclude that x=z from that information?

is that "permenantly finite" or something

For all n, if there is a 9 in the nth decimal position of 0.999..., then there is also a 9 in the n+1th decimal position.

From a recent post:

0.999... = 0.999...9 = 0.9 + 0.09 + 0.009 + ...

= 1 - 1 /10^n with n n integer starting at n = 1, then n increased continually, limitlessly aka infinitely where the pre-requisite number of nines that begins to qualify 0.999...9 is the largest number of consecutive nines to the right of "0." that you can or cannot generate with your brain, and from there --- n continues to increase limitlessly aka infinitely.

1/10^n is never zero.

1 - 1/10^n is never 1.

0.999...9 aka 0.999... is never 1.

 

What is a number?

From a recent post:

The number of nines in 0.999... is limitless, aka infinite aka inexhaustible.

It does not matter how many nines there are, 'infinite' quantity or not.

The "0." prefix guarantees magnitude less than 1.

The only way you can get a 1 from a (0.999... + x) operation is to add a /10^n scaled down version of '1' (ie. the 'x') to a limbo nine in 0.999...9 aka 0.999...

You will never get a '1' from 0.999... itself, because afterall, 0.999... is equal to 0.9 + 0.09 + 0.009 + ...

which is 1 - 1/10^n for the case integer n pushed to limitless aka infinite. And 1/10^n is never zero is an unbreakable fact.

So 0.999... is never 1 because 1/10^n is never zero.

 

1/10^(n) is the limit we are evaluating. 1/10^(n) = 0. Define n —> ∞ and the limit is equivalent to zero. In my opinion, ”but not for any integer/finite n” is overstated and it’s unlikely to reach someone who does possess the misconception (although on this subreddit, there’s the people who deny the limit altogether). Clarifying something should be integrated into a response gracefully and you should address the rest of the content of what you’re responding to instead of only stating a clarification (i.e avoid responding with a clarification only to nitpick or change the subject). I’ll conclude by saying that you shouldn’t start a dispute which isn’t original and reflective of value.

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I've never seen him ask a question to learn something. I don't mean those

Have you signed the contract?

Do you use your brain?

mock questions (even though I can't remember the last time SPP has asked any question, including these "insults").

He thinks that he knows it all yet we never see him trying to acquire new knowledge, or even asking in order to better understand what the person being asked means by their statements.

It's a pretty clear sign of his intellectual arrogance, narcissism and the Dunning Kruger Effect.

I won't be taking questions