What is this infinite fraction equal to? Is it undefined? You

>>8499804
I got this result too. It is really weird to one number like that be equal to 1.

>>8499800
undefined ofc

>>8499810
give me the qed

-1

guys, don't forget this shit is equal to 1/1/1/1...

>>8499800
-1/12

>>8499800
Did you know that everywhere exists additions of 0 and multiplications of 1???

>>8499833
(shhh, let them discover by themselves)

File: party_time.jpg (746KB, 1200x799px) Image search: [Google]

746KB, 1200x799px

To do this rigorously, you need to project onto a triadic semi-complete Chomper space, then perform the universal recomplication in the obvious manner to reach the result of unity.

>>8499800

Theta = 1/(0+Theta)

Theta = 1/Theta

Theta^2 = 1

Theta = 1

If you guys didn't get this you're retarded and should probably go back to /b/

>>8499830
good meme

>>8499841
So theta can also be -1?

>>8499841
Let's say
x = 1
= 1 / 1
= 1 / x
so x^2 = 1
so x = -1 or 1

this is how dumb you are lol

>>8499841
Theta = 1/ (0+1/(0+theta)) = 1/(1/theta)=theta

Theta has infinite solutions.

>>8499864
You're retarded

>>8499877
Another thread called me a retard too. Guess I am a retard.

>>8499800
that shit is childish

x = 1 / (0 + x)
x = 1

>>8499884
Well that's pretty honest from you.

>>8499808
brainlet

>>8499800
for people that actually don't know how to do this

[math]\theta = \frac{1}{0+\frac{1}{0+\frac{1}{0+\frac{1}{0+...}}}}
=\frac{1}{\frac{1}{\frac{1}{\frac{1}{...}}}}= \frac{1}{\theta}[/math]
note that:
[math]\theta > 0[/math]
we obtain:
[math]\theta = \frac{1}{\theta} \Leftrightarrow \theta^2 = 1 \Leftrightarrow \theta = 1 \quad \quad \quad \quad \square[/math]

>>8499817
qed

https://en.wikipedia.org/wiki/Continued_fraction

Mind blown

Rewrite it as [math] \theta = \frac{1}{\theta} [/math] and it's clear that this has two solutions, 1 and -1. Pretty interesting.

>>8500304
>θ2=1⇔θ=1
"no"

1/infinity

thus 1 / (-1/12)

turns into

1 * (-12/1)

thus, -12

QED

i don't know what is the biggest bait: the original post or -1/12 replies

>>8500409
Kek.

Let [math]\theta \,\in\, \mathbf R[/math].
[eqn]\theta \,=\, \frac{1}{0 \,+\, \theta} \,=\, \frac{1}{\theta} \quad\text{iff}\quad \theta^2 \,=\, 1 \quad\text{iff}\quad \theta \,\in\, \left\{-1,\,1 \right\}[/eqn]
In other words, your shit is undefined. As always, OP is a faggot.

how do you assign a value to this shit when all of the truncated fractions are 1/0

>>8499800
>>8500600

>>8499800
x = 1/(0 + x)
x = 1/x iff
x^2 = 1 iff
x = 1 or x = -1

Consider the partial fractions to discard -1 as an option.

x=1

>>8500365
>>8499860
>>8499826

No, you fucking pleblet.

Don't tell me none of you "high IQ people" ever saw infinite fractions in number theory? It is a trivial procedure to compute the partial fractions and see why -1 cannot be a solution.

>>8500304
\square

>>8500623
Please do compute the partial fractions.

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>>8499800
VERY IMPORTANT POST

Everyone who said the answer is 1 or -1 is wrong. What you have shown is that IF AN ANSWER EXISTS, then it must be 1 or -1.

However, every infinite fraction is irrational (google it). This means that theta is not well-defined (because if it were defined, it would have to be 1 or -1, a contradiction).

Alternatively, an infinite fraction is BY DEFINITION the limit of the sequence of finite continued fractions obtained by truncating after n levels. Since each such truncation has a zero in the denominator, every element of this sequence is undefined, so the limit is also undefined.

>>8499877
no he's not. He's wrong, but not any more wrong than the people who say the answer is 1.

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>>8499800
>infinite fraction
Is that right?

kind of lol at 1 or -1

it will oscillate as x = 1/x for x not = 1

>>8501518
Thank god. I was getting to the end of the thread and seriously feared no one had given a decent answer.

>>8500673
s1 = 1
s2 = 1
s3 = 1

If you want to be autistic then you can get the weird looking general form:

sn = 1/(0 + 1)^(n-1)

This looks weird but you need to re arrange

0 + 1/x = (0 + 1)/x

And then take the limit as n approaches infinity which is 1/1^infinity = 1

That algebraic solution you've maybe seen in numberphile videos is a good tool to find possible answers. Maybe you have a series of fractions that you can prove converges but cannot truly find what it converges to by taking the limit, so you prove it converges and use the algebraic method to find possible solutions. But alone it does not say anything.

It, if anything, says that if your infinite fraction converges, then it must converge to one of those values.

>>8501518
>every infinite fraction is irrational
so undefined is an irrational number now?

>>8500387
given that θ > 0 the statement is valid.

brainlet

>>8502162
wrong
>>8501518
right