🧵 >Has yet to be refuted
Anonymous at Mon, 20 May 2024 15:04:29 UTC No. 16184601
Claim: [math] 0.999_{\dots} \neq 1[/math]
Proof: We use induction. The base case is trivial: [math] 0.9 \neq 1[/math]. Next we introduce the notation that [math]0.9_n = \underbrace{0.9999999}_{n-\text{man
Now the inductive step: we assume [math]0.9_n \neq 1[/math]. Then trivially [math]0.9_{n+1} \neq 1 [/math]. It might help to notice that [math] 1 - 0.9_{n+1} \neq 0[/math].
This implies that [math]0.9_n \neq 1 \qquad \forall n\in \mathbb{N}[/math]
Finally, we define [math] 0.999_{\dots} := \lim_{n\to\infty} 0.9_n[/math].
[math]\therefore 0.999_{\dots} \neq 1 \qquad \square [/math]
Anonymous at Mon, 20 May 2024 15:14:08 UTC No. 16184613
>>16184601
Induction across the naturals doesn’t access infinity.
You proved that 0.9_n != 1 for all n in the naturals. What comes after that is an incorrect logical leap.
Anonymous at Mon, 20 May 2024 15:19:57 UTC No. 16184622
>>16184613
using your logic, 0.999... cannot be represented as a natural number since it contains infinitely many digits which isn't in N. so a number not in N is allegedly in N?
Anonymous at Mon, 20 May 2024 15:22:38 UTC No. 16184624
>>16184613
>what is Transfinite Induction
So do you believe in 0.999…=1? Or do you believe in Infinity? It can’t be both.
(Nobody say anything, let this credulist squirm for a spell as he tries to get his story straight.)
Anonymous at Mon, 20 May 2024 15:23:03 UTC No. 16184625
>>16184601
Your induction step is wrong. Quantum mechanics shows that for large enough n, 0.9_n = 1 because the world is discrete
Anonymous at Mon, 20 May 2024 15:29:10 UTC No. 16184631
>>16184624
>transfinite induction
Is this the newest wokie math?
Anonymous at Mon, 20 May 2024 15:51:12 UTC No. 16184648
>>16184622
illiterate rofl
>>16184624
> muh transfinite induction
lmao, ok retard.
OP’s induction does not actually ever reach the case where 0.999… has an infinite number of 9s. Infinity is not in the naturals, and the induction only ever iterates over the naturals.
The limit written after not being equal to 1 is a non sequitur and incorrect.
Otherwise, please, point me to the number between 0.999…. and 1.
Anonymous at Mon, 20 May 2024 16:55:48 UTC No. 16184712
>>16184601
Have you ever heard of intervals?
Anonymous at Mon, 20 May 2024 18:53:59 UTC No. 16184877
>>16184601
Best thread on /sci/ right now.
Anonymous at Tue, 21 May 2024 10:19:10 UTC No. 16185984
>>16184624
you were right
>>16184648
he squirming
Anonymous at Tue, 21 May 2024 12:28:17 UTC No. 16186116
>>16184625
But because of the uncertainty principle, it is sometimes possible that 0.999… > 1