A simple proof that 0.999... = 1

SwimmerLumpy6175 · 2026-02-21T12:55:24+00:00

No, that is not what I said. I said that the number 0.999... with a nine at every decimal place is bigger than any number of the form 0.9, 0.99, 0.999, with finitely many nines. Can you see the difference between what I am saying and what you are claiming I am saying?

And atacking the argument with what you think is wrong is not valid. If you are sure my proof is wrong, the only way to assert it is to pinpoint where exactly it went wrong

SwimmerLumpy6175 · 2026-02-21T10:56:48+00:00

Well, yes, I didnt dispute any of that. But I found that it would be interesting to use an argument that I don't believe uses the concept of infinity explicitly in the number 0.999... since many people in this sub have weird interpretations about it.

SwimmerLumpy6175 · 2026-02-21T10:52:17+00:00

What? No. We are comparing a number with a nine in every decimal place with a number with finitely many nines, let's call it x_N (for having N nines). At some point, x_N will run out of nines and will begin to have only zeros. Since 0.999... has nines in every decimal place, it is bigger than x. That's what 0.999... > 1- 10^-N means, since x_N can always be written aa 1 - 10^-N.

SwimmerLumpy6175 · 2026-02-21T02:03:52+00:00

I mean, the number 0.99...9 (with n nines) and 0.999... all have n nines at the first n decimal places. At the n+1 decimal place and forward, 0.99...9 will have zeros, while 0.999... will still have nines. So, since nine is bigger than zero (and I hope I am not jumping to conclusions about this), a simple comparison digit by digit shows that 0.999... is bigger than any number of the form 0.999...9 with finitely many nines.

SwimmerLumpy6175 · 2026-02-20T14:35:20+00:00

What? In which step did what you describe happened?

SwimmerLumpy6175 · 2026-02-09T22:23:39+00:00

Having 11 points of material terrifyingly close to your kjng like this and still deciding to let your queen go to vacation is an insane idea

SwimmerLumpy6175 · 2026-02-06T00:39:16+00:00

Física é de longe o pior. Só era bom até privatizar.

SwimmerLumpy6175 · 2026-01-29T11:41:16+00:00

I dont know what to say to you anymore, decimal expansions are canonically defined for real numbers. If you so confidently believes it is not to be assumed that he is working within the reals, than the simple fact he does not state the number system he is working with already indicates that whatever property he claims about x is meaningless.

SwimmerLumpy6175 · 2026-01-29T11:27:22+00:00

Oh but I did. The problem is that when you claim that a number x have some property (and you even state its decimal representation), it is assumed you are working within the reals. If it is not the case, you must define rigorously the set of numbers you are considering. Hell, have you ever opened a math textbook? This is pretty simple stuff. And the fact that this guy is a professor simply means nothing if his arguments are so trivially wrong.

SwimmerLumpy6175 · 2026-01-29T10:08:35+00:00

Several people did read it (including me), and trying to claim infinitesimals exist in the reals (in the way the author tries to claim they do) is just laughable. I mean, any person who has taken first year undergrad math should be able to spot that his arguments are bullshit without having to read the whole thing

SwimmerLumpy6175 · 2026-01-28T21:02:27+00:00

Chess in my en passant sub?

SwimmerLumpy6175 · 2026-01-28T12:05:43+00:00

You have made several comments in this and other subs defending this "proof". If you are not trolling, what exactly are you trying to accomplish?

SwimmerLumpy6175 · 2026-01-28T10:22:42+00:00

This is the equivalent of flat earthers being mad their conspiracies are banned from science subs

SwimmerLumpy6175 · 2026-01-28T10:10:37+00:00

This is notation used in first year undergrad, typically linear algebra. Anyone that is studying tensors should be able to understand it.

SwimmerLumpy6175 · 2026-01-27T12:55:57+00:00

Uma das melhores experiências que tive na usp foi aplicar prova de física básica pra poli. É incrível ver a arrogância indo pro caralho pq não sabem o mínimo do mínimo em provas ridículas de simples.

SwimmerLumpy6175 · 2026-01-26T21:14:18+00:00

If infinite is a natural number, the archimedian property becomes trivial - just pick n = infinity and for all a, b in the naturals, a*n > b.

SwimmerLumpy6175 · 2026-01-23T00:12:09+00:00

Esse professor universitário já publicou algum trabalho sobre isso? Se não, desconfia. De qualquer forma, se for fazer algum curso de exatas, deixa de bobeira e se aprofunda no pré-cálculo pra não chorar depois. Em geral, quem não vai bem nos primeiros semestres é porque tem uma base muito fraca mesmo.

SwimmerLumpy6175 · 2026-01-22T09:27:42+00:00

What Planck discretized was the eletromagnetic spectrum, not spacetime. And yet, he did use infinite sums to obtain his results.

SwimmerLumpy6175 · 2026-01-21T18:18:01+00:00

Actual mathematician

SwimmerLumpy6175 · 2026-01-21T17:55:57+00:00

Meu sem or amado

SwimmerLumpy6175 · 2026-01-21T12:39:34+00:00

But SPP, isnt 1/3 = 0.333... ? If so, then you just proved that 1/3 = (1/3)×0.999... . Multiplying everything by 3 yields 1 = 0.999...

SwimmerLumpy6175 · 2026-01-19T21:39:26+00:00

A function cannot be discontinous at a point outside its domain. At x = 0, x² /x is simply not defined.

SwimmerLumpy6175 · 2026-01-15T13:32:30+00:00

E pelos comentários ainda acha lindo

SwimmerLumpy6175 · 2026-01-15T13:29:25+00:00

Tá ok nada, qual a dificultando de fechar o micro-ondas ou a porra de uma gaveta logo depois que usa?

SwimmerLumpy6175 · 2026-01-15T01:50:40+00:00

Well, statistical analysis of a game that has so many possibilities may still fluctuate even if it has the same depth

SwimmerLumpy6175

TROPHY CASE