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/sci/ - Science & Math

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2106340 No.2106340 [Reply] [Original]

can someone explain this to me?

>> No.2106344

no

>> No.2106355

>inb4 "durr it's not"

Decimal representations of numbers aren't necessarily unique. The simplest way to see it is to observe that 1/3 = 0.333.... But 1/3 + 1/3 + 1/3 = 0.999.... = 1.

>> No.2106358

.999... = 9(1/10) = 9(1/10) + 9(1/10)^2 + 9(1/10)^3 ... = [9(1/10)]/[1-(1/10)]=1

>> No.2106726
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2106726

Forget math, all you need is faith to prove that!

>> No.2106748

1/3 = .333333...
2/3= .6666666...
3/3= .9999999...

>> No.2106783

x = .999...
10x = 9.999...
10x - x = 9.999... - .999...
9x = 9
x = 1

thus x = .999... = 1

>> No.2106795

There are no numbers between .9999999... and 1, thus they are equal.

>> No.2106806
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2106806

>> No.2106823

1 - 0.999999999999999999999...

= 0

>> No.2106850

Wow, didn't know /sci/ was filled with trolls just like /b/.

.99999...!=1

>> No.2106977

0/10

at least make up some retarded evidence to reinforce your feigned ignorance

also rules 1 and 2

>> No.2106993

<div class="math">0.999 \dots= \lim_{n\to \infty} 0.\underbrace{99 \dots 9\,}_{n} = \lim_{n\to \infty} \sum_{k=1}^n \frac{9}{10^k} = \lim_{n\to \infty} (1 - \frac{1}{10^n}) = 1 - \lim_{n\to \infty} \frac{1}{10^n} = 1</div>

>> No.2107005

>>2106993

That bottom limit goes to zero not one.

>> No.2107036

>>2107005
>implying 1-0 doesnt equal 1

>> No.2107219

>>2106795
As said. If you can fit some kind on number between x and y, they are different numbers. Like 1 and 2, you can place 1,5 between them. But you can't do that in case on 0.9999999... and 1.

>> No.2107239

Plenty of proofs in this link:
http://qntm.org/pointnine

>> No.2107265

Here's a more general approach to it instead of a mathematical approach. If you say these numbers aren't the same you are saying that there is a difference between these two numbers. That is, you can subtract one from the other and the answer would not be 0. A common assumption to this difference is .000......1. That is, an infinite amount of 0's after the decimal place followed by a 1. However, this number does not exist. You cannot simply have something after an infinite amount of 0's. You can't stop somewhere and say "I think I'll put a 1 here now", because if you do that, you no longer have an infinite amount of 0's. An infinite amount of 0's followed by a 1, is just an infinite amount of 0's...or zero. The difference between .999... and 1 is 0, thus they are the same number.