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/sci/ - Science & Math

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5667906 No.5667906[DELETED]  [Reply] [Original]

I solved pic related and my result is 0.999... (repeating) but my teacher says it's 1.

Who is right? Is my teacher a retard?

>> No.5667917

0.999 = 1
This is a fact, look it up on wikipedia.
It is literally not up for debate.
Please stop with these threads they happen every day

>> No.5667921

>>5667906

Is the sum of a converging sequence the same as its limit?

>> No.5667944

>>5667906
Your teacher is wrong.

>>5667917
>It is fact because it is on wikipedia
Argument by authority doesn't work in math.

>>5667921
No.

>> No.5667946 [DELETED] 

You're both right. <div class="math">0.999\ldots=0.9+0.09+0.009+\cdots=\sum_{k=1}^{\infty}\frac{9}{10^k}=\lim_{n\to\infty}\sum_{k=1}^n \frac{9}{10^k}=\lim_{n\to\infty}9\cdot \frac{\frac{1}{10}- \frac{1}{10^{n+1}}}{1-\frac{1}{10}}=9\cdot \frac{\frac{1}{10}}{1-\frac{1}{10}}=1</div>

>> No.5667949

You're both right. <div class="math">0.999\ldots=0.9+0.09+0.009+\cdots= \sum_{k=1}^{\infty}\frac{9}{10^k}= \lim_{n\to\infty} \sum_{k=1}^n \frac{9}{10^k}= \lim_{n\to\infty}9\cdot \frac{\frac{1}{10}- \frac{1}{10^{n+1}}}{1-\frac{1}{10}}=9\cdot \frac{\frac{1}{10}}{1-\frac{1}{10}}=1</div>

>> No.5667953

>>5667944

Sum not equal to limit..

I believe you are wrong. The only way to settle this is a duel to the death.

>> No.5667963

I think this is an undecidable question.
It depends on whether or not you think the infinitely insignificant remainder matters or not.

>> No.5667961

Here are a few reasons why 0.999... and 1 cannot be equal:

>a rational number cannot equal an irrational number
>the limit is only a hypothecial point in infinity that is never truly reached
>a number cannot have two decimal representations because decimals are a linearly ordered set
>the difference 1 - 0.999... is 0.00...01 > 0
>every "proof" of them being equal turned out to be a fallacy of circular reasoning

>> No.5667965

>>5667961
Thanks tripfag.

I'm gonna call out my teacher on his bullshit.

>> No.5667968

>>5667961

The fact that you have (not trolling) in your name is conclusive proof you are in fact a Troll.

>> No.5667971

1/3 = 0.333...
1/3 x 3 - 1
0.333... x 3 = 0.999...
0.999... = 1

Oh, and I don't think anybody believes your little student-teacher anecdote. We all know you're simply making it up because you want a controversial topic.

>> No.5667977

>>5667961
>>every "proof" of them being equal turned out to be a fallacy of circular reasoning
This doesn't prove that 0.999... and 1 aren't equal.