/prog/rammer here, need urgent help

hello /sci/, long time no see
There is currently a troll on /prog/, and would greatly appreciate your help.

Basically, the troll is trying to prove that 0.999~ =/= 1
Here are some of his arguments
http://stormtower.invisionplus.net/?mforum=stormtower&showtopic=97

I'm wondering if the maths genius' on this board can rip him apart? Thank you

>>79,80
( ´_ゝ`)

>>79
[not quoting properly]
´L_`

>>82
I only come here from /b/ now and then to point out how retarded u gaiz are, so I don't know about your fancy bbcodes.

/irony

>>77
1. Fact: Wrong.
2. Fact: True, better then the last fact at least.
3. Wrong, wrong and wrong.
2. How the fuck did you go back to 2? Anyway, this point does not follow from 2 in any logical sense, it's true, but faulty reasoning.
3. No. 0.999...=1 without any sort of successor function
4.Just what the fuck.


You seem to have assumed the reals are countably infinite, to be able to inductively reach any of the from this silly "sucessor" function, which makes no sense anyway.
How can you increase the last digit of an infinite sequence?

What s(pi)?

To repeat, Maths is harder than you think.

And I call it maths because it's a series (multiple) of interwoven disciplines. And also cause I'm a eurofag.

>>84

.0000000000000...1 -> .000000000000...2

AM I RITE /SCI/ ?

>>86
obvious troll

>>84
You said it yourself that you can't increase the last digit of an infinite sequence, so what's the sense in:

1 - 0.999... = 0.000...1

Would not that last one in 0.000...1 be at the end of an infinite series?

Or better yet, does not your statement imply that you can't decrease the last digit of an infinite series?

>>87
Thank you for pointing that out, I would have taken him seriously if you hadn't.

http://en.wikipedia.org/wiki/Infinitesimal

look it up bitches, 0 is the only infinitesimal number in the reals. if you want to work with infinitesimals, fine, you better get used to some of the following ideas

x^n = 0 does not imply x = 0
it is possible that two numbers are neither equal nor not equal.

so what makes you more uncomfortable?

1 = 0.999...
or the two statements above?

>>92
Explain to me what 3 * (1/3.....) is

>>89
y/w

Not this thread again. Jesus Christ.

>>92
lolwut?
>>93
What do you mean by (1/3...) ?
>>96
I concur.

>>97
1/3 = 0.333...
1/3 + 1/3 + 1/3 = 1
0.333... + 0.333... + 0.333... = 0.999...
THEREFORE
0.999... = 1

>>98
I'm not sure why this was directed at me....All I was asking about was what (1/3...) meant, particularly the ellipsis. I completely agree with your line of reasoning.

100 GET

God damn, /sci/ never changes.

>>101
It wasn't disproven, just based on a fact that isn't accepted by the unenlightened.

that because .999 is an approximation of 1/3      so .999 is an approximation of 1   therefor does not equal 1 but is an approximation.

>>100

hahahaa... yup

limits, definition of real numbers...

.999... = .999...

1=1

The two numbers are infinitesimally close, but it deals with fucking infinity, which no one can come to an agreement on.

Also, I love how all the programmers got worked up at >>7 for saying what he said.  He didn't even say he was a mathematician.

tl;dr programmers are butthurt.

>>106

After all, infinity was only formalized more than 50 years ago for most of its forms, and up to 150 years ago for the oldest. And that no common definition of real numbers see a difference between the two.

>>99
So you finally admit you don't know what your talking about.
I rest my fucken case.

>>108
No, I'm actually fairly sure I said nothing to imply that I don't know what I'm talking about. I asked what (1/3...) means, as I'm fairly sure the ellipsis is meaningless, and I didn't say that RedCream's proof was a proof, I just agree with the particular line of reasoning.

basically all rationals can be written as a fraction or in a decimal form which eventually terminates or recurs. and vice versa.

.99999... is a completely full glass of water. You cannot add any more water without it overflowing.

can we all please STFU about this?

>>113
Splitting hairs here. It's just an analogy. Fine. .999... is a completely full glass of a substance that can be divided into infinitely small parts. My point is IT'S STILL EXACTLY ONE (as in 1) GLASS.

With every decimal place completely full no finite number can be added to .999... without it making more than 1.