0.999999... = 1?

What the fuck. Why is that true. They got different numbers in them.

>>188
>>189
Yes, any recurring decimal number is rational. You can convert any recurring decimal x with period length n to a rational number just by taking 10^n x - x:

   x = 0.18181818...
100x = 18.181818...
 99x = 18
   x = 18/99 = 2/11

>>190


0.9999... is rationel because it have a template and because I can prove it.

.9999... * 10 = 9.9999...
.9999... * 9 = 9
.9999... = 1

And 1 is rational.


And i am not a math studiant. i am a math teacher. And this fucking .99~8 or 0.000...1 DONT EXIST! I'ts easy to prove than 10^-x with < -> infinite = 0. Not 0.00...1

>>201
NO U
0.181818... < 2/11 LOLOLOL

>>202
They're letting twelve year olds teach math know?

Well, at least he's right.

*now. Fuck.

MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS MATH IS FOR FAGGOTS

0<1=FAGGOTS

The best I can say is that lim(n -> +infinity- [infinity greater than zero, approached from the lesser side]) { sigma(x=1; x <= n) {9/(10**n)}  }== 1.

That is to say, as you increase the number of 9 that follow 0. in the expression 0.999999, the value of that expression approaches 1. 0.999... == 1 only in the case that you have iterated an infinite number of 9 after the decimal.

uhhhh someone else finish what i'm saying if i'm going in the right direction. or am i just blowing air out of my ass

oh and also
.9~ + epsilon == 1

defining epsilon, the infinitesimal, is an exercise left to the reader

OMFG 0.999~ = 1 NOW SHUT THE FUCK UP STUPID NIGGERS

>>208

You're absolutely correct.

>>209

In that expression, epsilon = 0

I defined epsilon for you, lawl

>>210
Hey guys in non-standard analysis 0.999... != 1.  Now STFU.

>>209
Epsilon is not the infinitesimal here. That epsilon is just zero. If you were trying to refer to epsilon-delta limit proofs, that epsilon is NEVER an infinitesimal.

Why do people keep saying infinitesimal when they have no idea what it means?

I AM A HARVARD MATH PROFESSOR AND I THOUGHT I SHOULD RESPOND TO THIS TO SET THE RECORD STRAIGHT. 0.9~ IS NOT EQUAL TO 1 BECAUSE YOU CAN NEVER FINISH WRITING DOWN ALL THE 9'S. IT'S THAT SIMPLE.

I am sure that you left some behind and the next guy that sits down will get HIV.

INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL INFINITESIMAL

>>214
I don't need to write down the 9's, I just write "1".

I wants lots and lots of some delectable pot!

Marijuana MUST be legalized.