If this proof for 0.999... = 1 does not convince every singl

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im not convinced
you're just another brainlet

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>>8972986
>journalofsci
d r o p p e d

>>8972986
>Use Imgur for images
Now [math] \color { red } { THIS } [/math] is some next level shitposting.

>>8972986
If this had a finite number of decimals, the last is always zero, eg. 0.999+0.111=1.110
If we apply the same logic, it always means that (S+0.111...)<1.111...
Subtract 0.111... from both sides and you get 0.999...<1 which is the logical fucking thing, you mongoloid.

>>8973014
>If we have a finite set, it can never be equivalent to one of its proper subsets
>Now if we apply that same logic, it means that an infinite set can't be equivilent to one of its proper subsets
>Which is the logical fucking thing, you mongoloid
Wew lad.

>>8972986
Journal of sci is a platform for all of us to clearly express our ideas and promote them in a more legitimate way. We NEED this place that is protected from the scientific establishment. And we need more intellectual people to share their best ideas, this website will be HUGE, it will be the hub for the world's most cutting edge ideas.

I am working on a new theory of philosophy and science that will destroy the scientific community.

This theory will explain the nature of reality, prove free will, and solve the mind/body problem. Not even kidding.

The theory is all based on abstractions. I have been working on these ideas for 5 years, and later this week I am going to publish the shortest paper I can explaining these ideas.

If needed, I'll write an entire book, but hopefully people will understand the argument in a short paper. I'm going to be laying the foundation work paper on journal of sci later this week.

s = 0.9999999...
10s = 9.9999999...
10s - s = 9.999... - 0.999...
9s = 9
s = 1

>>8973045
This uses multiplication and division, Camino's proof only uses addition and subtraction.

That's a contradiction and just means you made a mistake

>>8973028
So you want to be a worse version of Vixra. How is that possible?

>>8973045
I also watch mathologer

>>8972986
Is there anyone who doesn't think that? That's what was taught to us in university.

You can never find a number x that 0.999...+x=1, then 0.999...=1. That's because in order to obtain 1 you would need x to be 0.0...infinitezeros...1 but that's not possible, the 1 would make it a finite number and there will always be 9s after the 1 in x

>>8973142
x = 0

>>8972986
>a + ... + b = b + ... + a
I'm not a pure mathfag but I'm pretty sure they learn the Riemann rearrangement theorem early on in Analysis.

>>8973144
Yes, i forgot to say x different from zero :)

1/3=0.33333333....
2/3=0.66666666...
3/3=0.999999999
But n/n is defined as 1
Therefore 0.999999....=1

>>8973243
Brainlet. Rearangment only apples to CONDITIONALLY CONVERGENT series. All these have positive terms so that is not the case.

If you don't believe me, find a rearrangement that results in a different number.

Yeah that's what I thought.

>>8972986
Just look at [math](x_n) \in1, x_i=1 \ \forall i \in \mathbb N[/math] and [math]y_n = \sum_{i=1}^{n}10^{-i} \cdot 9, (y_n)\in 0.999...[/math] obviously [math]\underset{n \to \infty}{lim}x_n-y_n=0[/math] (simple calculation.)
Then you have [math]y_n\in 1\Rightarrow 0.999...=1[/math] qed.

Simply applying the definition of equality is enough. Your proof is missing some serious steps which require some real analysis (e.g. where you are changing the order of the summation without even mentioning why that works or claiming your series converges without giving a proof).

>>8973756
It's easier to see that the series converges than it is to try to make people understand the messy language of limits, because people who don't agree will insist that it never actually reaches zero.

No website has made me want to puke this bad in years.

>>8973586
1 + 1 + ... + 2 = [math]\omega + 2 \neq \omega[/math] = 2 + 1 + ... + 1

You can't reject the existence of limit ordinals without giving up the ability to define R.
Addition of infinitely many expressions is not commutative in general. That's why the Eilenburg-Mazur swindle is nontrivial.

>>8973125
>Is there anyone who doesn't believe the dogma they are taught?
Whether or not I agree about the subject at hand your argument is utterly disgusting.

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>people still think .9999 does not equal 1

Brainlets.

>>8974358
Can you even read?

>find a rearrangement that results in a different number

All you did was post a divergent series.... that has nothing to do with the proof. You cannot rearrange the ACTUAL NUMBERS used in the proof because they are convergent.

Go ahead and try to rearrange any convergent series to get a different number... you will fail miserably. And everything in the proof is convergent.

>>8974532
>And everything in the proof is convergent.
Then why isn't there a lemma where the convergence is established, since we both agree that convergence is a necessary condition for the proof to be sound?

>>8973782
But that is just stupid.
You can not explain someone why two real numbers are equal if he doesn't know what a real number is.

>because people who don't agree will insist that it never actually reaches zero.
Then these people do not believe that the real numbers exist.

>>8972986
That's too complicated.

The idea is much simpler.

Theorem:

Let a,b in Q. a = b if and only if for all e in Q greater than 0, |a-b| < e.

The right side of the implication is evident. Now assume that for all e in Q greater than 0 |a - b| < e and that a != b, assume b < a, then a - b = c is greater than 0 and |a - b| < c/2. Thus a contradiction.

In other words, 2 rationals are equal if their difference is arbitrarily small. Thus 0.999999... = 1.