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Anonymous Sat 02 May 08:13:39 2020 No.11627716 View Reply Original Report

Quoted By: >>11627725 >>11627741 >>11628299

Hey, math novice here that's trying to self-educate.
Was wondering something.

I know 0.999... = 1 I'm not disputing that at all.
But if that's the case then 0.999.../2 should equal 0.5 right?
So my question is how does an infinite number become a finite one, what causes that infinity to collapse?
Probably just missing something but I'd like to learn what that is if it's the case

Anonymous

Anonymous Sat 02 May 2020 08:18:10 No.11627725 Report

Quoted By: >>11627729

>>11627716
An infinite number is by definition, not finite. Learn words.

Anonymous

Anonymous Sat 02 May 2020 08:19:43 No.11627729 Report

Quoted By: >>11627734

>>11627725
I didn't say it was?
Why the hostility man I'm just trying to learn.

Anonymous

Anonymous Sat 02 May 2020 08:20:21 No.11627730 Report

Quoted By: >>11627738

This question gets asked a lot here and it is unintuitive. If you really want to understand this I recommend you take notes on and intuitively understand the epsilon delta definition of a limit; the answer is not mind blowing as you might want it to be.

Anonymous

Anonymous Sat 02 May 2020 08:22:54 No.11627734 Report

Quoted By: >>11627740

>>11627729
Numbers don't become other numbers. They are just there.

Anonymous

Anonymous Sat 02 May 2020 08:25:18 No.11627738 Report

Quoted By: >>11627759

>>11627730
>intuitively understand the epsilon delta definition of a limit
I'm probably a little far from that but I'll keep it in mind.
>not mind blowing as you might want it to be.
Nahh I don't have any expectations I was just thinking about it and wondered if I was missing something. It's interesting stuff though.

Anonymous

Anonymous Sat 02 May 2020 08:26:19 No.11627740 Report

Quoted By: >>11627743

>>11627734
Okay? My question still stands, where does the infinity go?

Anonymous

Anonymous Sat 02 May 2020 08:27:28 No.11627741 Report

Quoted By:

>>11627716
>0.999.../2 should equal 0.5 right?
nope it's 0.4999...

Anonymous

Anonymous Sat 02 May 2020 08:28:20 No.11627743 Report

Quoted By: >>11627751

>>11627740
No it doesn't. What infinity are you on about? 1 is a finite number.

Anonymous

Anonymous Sat 02 May 2020 08:32:12 No.11627751 Report

Quoted By: >>11627754

>>11627743
But 0.999... isn't?

Anonymous

Anonymous Sat 02 May 2020 08:33:43 No.11627754 Report

Quoted By: >>11627758

>>11627751
0.999... is finite. It is equal to 1, which is finite.

Anonymous

Anonymous Sat 02 May 2020 08:36:30 No.11627758 Report

Quoted By: >>11627770

>>11627754
But doesn't it have infinitely repeating nines? How can something that is known to have infinitely repeating digits be finite?

Anonymous

Anonymous Sat 02 May 2020 08:36:58 No.11627759 Report

Quoted By: >>11627763

>>11627738
No if you can understand algebra you can pick apart this proof; it still isn't easy to wrap your mind around but I at least hope you are hasty to plant the seed.

Anonymous

Anonymous Sat 02 May 2020 08:40:09 No.11627763 Report

Quoted By:

>>11627759
I'll look into it now then, thanks anon.

Anonymous

Anonymous Sat 02 May 2020 08:49:51 No.11627770 Report

Quoted By: >>11627777

>>11627758
That doesn't make it infinite. Any real number is by definition finite. It does have infinitely many repeating 9s. What does that mean? We can write it as $0.\overline{9}=\sum_{n=1}^{\infty}\frac9{10^n}.$
>But how do we evaluate a sum with infinitely many terms?
Well often we can't, but in the case we have here, we can. We consider the partial sums $\sum_{n=1}^m \frac9{10^n}$ and see what happens as we increase m.
Clearly as m gets larger and larger, we get closer and closer to 1. The partial sums never exceed 1, but they get arbitrarily close to 1. Since the partial sums get arbitrarily close to 1, we say that they are equal.

Anonymous

Anonymous Sat 02 May 2020 08:55:09 No.11627777 Report

Quoted By: >>11627802 >>11627816 >>11627817

>>11627770
>Any real number is by definition finite.
Does that mean pi is finite?
What makes something infinite if not infinitely repetition?

Anonymous

Anonymous Sat 02 May 2020 09:14:58 No.11627802 Report

Quoted By: >>11627813 >>11627842

>>11627777
do you know what a limit of a sequence is ?

Anonymous

Anonymous Sat 02 May 2020 09:20:24 No.11627813 Report

Quoted By: >>11627921

>>11627802
Vaguely, they didn't teach calculus at my high school for some reason.

Anonymous

Anonymous Sat 02 May 2020 09:21:26 No.11627816 Report

Quoted By: >>11627844

>>11627777
>What makes something infinite
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

Since pi is overwhelmed by 3.2, not that infinite

Anonymous

Anonymous Sat 02 May 2020 09:21:38 No.11627817 Report

Quoted By: >>11627841 >>11627844

>>11627777
Pi is finite for a given arbitrary precision.

Anonymous

Anonymous Sat 02 May 2020 09:39:11 No.11627841 Report

Quoted By: >>11627870

>>11627817
wat
pi is finite, but it cannot be represented exactly with decimals. Or by a polynomial. do you mean you can approximate it up to an arbitrary precision, given unbounded memory space?

Anonymous

Anonymous Sat 02 May 2020 09:39:43 No.11627842 Report

Quoted By: >>11627921

>>11627802
the limit of (1, 1/2, 1/3, 1/4, 1/5,...) is zero, because the sequence eventually gets to zero up to an arbitrary precision. the sequence is infinite in the sense that it consists of an infinite amount of data (very vaguely). but the limit is perfectly finite, it's the finite number 0.
a decimal representation is a certain sequence, and the number it is supposed to represent is the limit (of a slightly different, but related sequence).
it doesn't make much sense to say that number is finite or infinite. it's only the decimal representation (the sequence) which can be finite or infinite. but the number itself (the limit) is always finite.
for example the number 1 has two decimal expansions, one is finite and one is infinite. both of them produce 1 as a finite object.
the number Pi has only an infinite decimal expansion. but again, Pi itself is finite.

Anonymous

Anonymous Sat 02 May 2020 09:40:49 No.11627844 Report

Quoted By: >>11627862 >>11627870

>>11627816
>>11627817
So that means there's a difference between "finite" and "terminating" right?

Anonymous

Anonymous Sat 02 May 2020 09:58:48 No.11627862 Report

Quoted By: >>11627871

>>11627844
of course? Assuming that what you mean by "terminating" is associated to a representation of a finite number.

Anonymous

Anonymous Sat 02 May 2020 10:04:39 No.11627870 Report

Quoted By: >>11627878

>>11627841
Yes, the approximation will be finite to whatever precision OP desires, theoretically. By arbitrary precision I mean representation to some arbitrary number of decimals. This does not mean 'exactness' which I understand as the complete solution. I think OP's understanding is due to his wanting to get a final result, e.g. 0.999... / 2 = 0.5, while it would simply suffice to say 0.999... / 2 is the exact result.

>>11627844
"Terminating" in your sense I suppose means whatever decimal you end up writing at the end when you don't want to write any more decimals and have rounded. If you approximate any value and "terminate" it, then the approximate value is finite to whatever precision you ended up with, but that does not mean that the original value was necessarily finite. I think the terms are not really comparable.

Honestly I am not sure if OP is just trying to troll, but in that case, good job.

Anonymous

Anonymous Sat 02 May 2020 10:05:45 No.11627871 Report

Quoted By:

>>11627862
I see, I may have started this thinking those two things meant the same thing.
Like I said, novice.

Anonymous

Anonymous Sat 02 May 2020 10:08:29 No.11627878 Report

Quoted By: >>11627949

>>11627870
>Honestly I am not sure if OP is just trying to troll, but in that case, good job.
Does it actually seem like a troll?
No, I'm not. I guess feel free to call me a dumb dumb poopyhead for wanting to learn more about something I don't know a ton about.

Anonymous

Anonymous Sat 02 May 2020 10:27:05 No.11627906 Report

Quoted By:

The representation of a number having an infinite amount of digits is not the same thing as the number itself being infinite. All irrational numbers have infinite decimal representations.

Furthermore, there is no "collapsing", this is not physics. Infinity is not some really "wow cool I love science" thing, it needs a concrete definition which, while varying from case to case, often shares fundamental properties. From this definition results are forced on us.

Anonymous

Anonymous Sat 02 May 2020 10:34:07 No.11627921 Report

Quoted By:

>>11627842
was meant for >>11627813

Anonymous

Anonymous Sat 02 May 2020 10:48:30 No.11627949 Report

Quoted By:

>>11627878
if you're OP, you also have to understand that topics about 0.999... ** 1 are the ultimatest troll here, hence our relative agressivity. Nothing personal, kid.

Anonymous

Anonymous Sat 02 May 2020 13:41:16 No.11628299 Report

Quoted By: >>11628397

>>11627716
There is really no relevant difference between a terminating decimal and a repeating decimal. Every number with a terminating decimal representation also has a non-terminating decimal representation with repeating 9s (except for 0). So it's really the non-terminating decimals that are weird.

Think about decimals as instructions for where to go on a number line. If you start at 0 and then move 0.9 units to the right, then 0.09 units to the right, etc., you are going to the same place as if you started at 2, then move 0.9 units to the left, then 0.09 units to the left. Starting at 0 you are going to 0.999... and starting at 2 you are going to 1.000... Since you traveled the same distance to get to those numbers, and 1 is right in the middle of 0 and 2, those numbers must be equal. You are just approaching 1 from different directions.

Anonymous

Anonymous Sat 02 May 2020 14:11:02 No.11628397 Report

Quoted By: >>11628412 >>11628417

>>11628299
>Think about decimals as instructions for where to go on a number line. If you start at 0 and then move 0.9 units to the right, then 0.09 units to the right, etc., you are going to the same place as if you started at 2, then move 0.9 units to the left, then 0.09 units to the left. Starting at 0 you are going to 0.999... and starting at 2 you are going to 1.000... Since you traveled the same distance to get to those numbers, and 1 is right in the middle of 0 and 2, those numbers must be equal. You are just approaching 1 from different directions.
your intentions were good, but the execution is screaming for "YEAH YEAH BUT I'M ONLY APPROACHING ONE IT'S NOT LIKE I ACTUALLY GET THERE" reply.

Anonymous

Anonymous Sat 02 May 2020 14:18:01 No.11628412 Report

Quoted By:

>>11628397
How do you know what his intentions are, for all you know he wants to use math to bring back the third Reich.

Anonymous

Anonymous Sat 02 May 2020 14:19:00 No.11628417 Report

Quoted By:

>>11628397
That's fine though, since the point is simply that these processes approach the same point. Saying 0.999... is different from 1 would mean 1.000... is different from 1.

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