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/sci/ - Science & Math

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5607140 No.5607140[DELETED]  [Reply] [Original]

Tell me /sci/ knows this already cuz /b/ went apeshit...

Pic is algebraic proof that .999... = 1.

>> No.5607143
File: 11 KB, 362x346, math2.png [View same] [iqdb] [saucenao] [google]
5607143

Proof with infinite series.

>> No.5607146 [DELETED] 

10x should = 9

>> No.5607148 [DELETED] 

>>5607146
please explain. show your steps.

>> No.5607149

<div class="math">0.999... = \lim_{n \to \infty}0.\underbrace{9999...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.5607151

>>5607140

Yes we know this. It comes up every so often. There are loads of other proofs that 0.9999... = 1

>> No.5607153 [DELETED] 

>>5607146
.9 (with the bar over it) indicates that the 9's repeat forever, it is not simple .9
was that the confusion?

>> No.5607157

>>5607149
please must tell me how to math font!

>> No.5607167

Bithcs don't know about my Infintesimals.

>> No.5607171
File: 47 KB, 408x410, efficient.gif [View same] [iqdb] [saucenao] [google]
5607171

>> No.5607172
File: 243 KB, 3600x1300, 1356729294151.png [View same] [iqdb] [saucenao] [google]
5607172

>>5607157

>> No.5607173

>>5607167
I do not.
What course is it discussed in?

>> No.5607178

>>5607172
Did we just become best friends?

>> No.5607179

>>5607173

HyperReal Analysis.

>> No.5607180

>>5607140
>algebraic proof
That is not a proof
To prove .9999....*10=9.99999.... you need to assume .999....=1. Therefore you proved NOTHING. Read some Rudin or get the fuck out of /sci/

>> No.5607184

>>5607178
...I'm not even the guy you asked

>> No.5607186

>>5607143
you can't prove geometric series converge without assuming .9999...=1.

>> No.5607191

>>5607172
This Josef doesn't seem to be a shitposter. I didn't know there were others like Organic Euphoria out there. I always thought tripfags had to be like EK.

>> No.5607203

>>5607191
Don't overgeneralize

>> No.5607209

>>5607180
He is using equivalent operations.
If he made false assumption he wouldn't get an obviously true result

>> No.5607216

>>5607180
That's a valid proof, fucktard

>> No.5607217
File: 4 KB, 132x146, 1358225202434.jpg [View same] [iqdb] [saucenao] [google]
5607217

>>5607180

>He doesn't know how to multiply by 10!

>> No.5607228

>>5607216
not completely

>> No.5607235

>>5607228

>Performs valid mathematical operations.
>Reaches a conclusion
>This conclusion is consistent with all other established mathematic

How is it not a valid proof.

>> No.5607236

>>5607216
No it's not. It assumes the decimal construction of the real numbers which assumes .999...=1. GTFO if you don't even know babies first analysis

>> No.5607243

>>5607235
it's valid enough for me, but it's not 100% rigorous. the proof in
>>5607149
is completely valid

>> No.5607258

>>5607191
hey come on

>> No.5607267

>>5607235
>Performs valid mathematical operations
>established mathematic

what the fuck are you taking about. To show that the decimal construction satisfies the real number field axioms, you MUST assume that .999...=1. So it's only a valid operation iff .999..=1 and you can't use it to prove .999..=1.

see http://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Stevin.27s_construction

>> No.5607278

>haven't come here in 6 months
>see this thread
Glad to see people are still hellbent on making this board a shithole.

>> No.5607281

The only thing that i am not sure about in OP's picture if it is a valid operation to subtract that 0.999... from 9.999... Isn't it impossible to withdraw infinite series from eachother?

>> No.5607289

>>5607149
>0.999... = lim
>limit
>an infinite series is equal to its limit
top lel

Nothing says whether it reaches it or not.
The infinite sum of 1/(2^n) has 1 as a limit, but obviously never reaches it.
And 1/x never reaches 0, even though it's its limit. It just approaches it.

>> No.5607299

>>5607289
I don't think you know how limits work

>> No.5608352
File: 117 KB, 600x602, 1312184615448.jpg [View same] [iqdb] [saucenao] [google]
5608352

>>5607140
that statement and its discussion is as meaningless as it can get, both in practice and in theory, tell me an expression that would end up giving me that number instead of 1...

it just shows our inability to handle the infinite when we "turn it into a real value".

If anything lim(0.99...) = 1, if that does even make sence

>> No.5608363
File: 193 KB, 750x756, 1333087666240.jpg [View same] [iqdb] [saucenao] [google]
5608363

>> No.5608370

>>5608363
>infantile cartoon