[eqn]displaystyle zeta left( sum_{k=1}^{infty} frac{9}{10^k} right) = zeta(1) = infty[/eqn] Therefore...

[eqn]\displaystyle \zeta \left( \sum_{k=1}^{\infty} \frac{9}{10^k} \right) = \zeta(1) = \infty[/eqn] Therefore, [math]\displaystyle 0.999\ldots = 1[/math]

I kek'd

>0.999...=infinity so 0.9999...=1

lmfao anime damsel you are high AF right now

>lmfao anime damsel you are high AF right now
nope, you are you fucking brainlet

you just took an infinite series and then concluded that 0.999...=1 now go back to your shit gween tea cartoon.

[eqn]\zeta(-4)=\zeta(-2)=0[/eqn]

Therefore, [math]-4=-2[/math]

W-what are you trying to say?

are you seriously implying that f(x)=f(y) => x=y is true?

fucking brainlets

yes. the only pole of the riemann zeta is 1

Why should this be true though?
[math]\displaystyle \zeta \left( \sum_{k=1}^{\infty} \frac{9}{10^k} \right) = \zeta(1)[/math]

It is obviously true if your conclousion is true but that is a pretty awful proof then.

this, the proof already assumes that 0.9999... = 1

why don't you compute it?

its not possible without the knowledge that 0.999..=1.

>It is obviously true if
It's not true. The function isn't define at [math] z=1 [/math]. There is no valid equation involving the a value [math] \zeta(1) [/math].

His proof goes 0.999...=1 therfore

\displaystyle \zeta \left( \sum_{k=1}^{\infty} \frac{9}{10^k} \right) = \zeta(1)

therfore 0.999...=1.

What is not obvious there, the middel part is irrelevant, his asumption is the same as his conclusion.

>isn't defined
it's a meromorphic function with a pole of order 1 at 1, genius

What if there is a 0.0.....001?

What are you trying to say? Saying it's a pole is also just saying it's not defined there, plus saying it's well defined in a neighborhood of that point.

no. there are different kinds of isolated singularities of holomorphic functions. a pole of order 1 is a very specific one. it means the function can be written as a power series at point 1 as

[math] \sum_{i=-1}^\infty a_i (x-1)^i [/math]

it's not that it's just "not defined" because it doesn't take a value in C, it literally takes infinity as a value at that point, an infinity with a very specific behavior.

YOU WHORE!
TAKE THAT BACK

>What if there is a 0.0.....001?
Excellent question.
What if there was a virtual 1?

...

Go count primes with Cocoa instead of doing this useless shit.

What secret does Cocoa have about the Zeta function that she does not want to tell us? She counts primes too quick.

Is there a reason that post-millenium anime girls are starting to look more and more like babies?