/sci/ - Science & Math

Previous Thread >>10607175

>>10610385
Why are you so pretentious in writing everything in a math environment?

>>10610419
What do you mean?

>>10610385
So that's basically Rule 60 of 1D Cellular Automata

>>10610385
Solution:
First do it for S_0=\{0\}. S_{2^n} should work.
Induction should be able to prove that.

Then remember that [math](P(X),\Delta,\cap)[/math] is a boolean ring (you just need that the symmetric set difference is commutative, associative and 2a=0). Then
[math]S_{n+1}=S_n\Delta 1+S_n[/math], and
by induction
[math]S_n=S_0\Delta a_1+S_0\Delta...\Delta a_n+S_n[/math] for {0,a_1,...,a_n} the n iteration of {0}. Then every 2^n such that 2^n>maximum of S_0 works.

[math] a\in S_{n+1} \iff [a-1\in S_n] \lor [a\in S_n][/math]
If [math]a\in S_0[/math] then also [math]a\in S_n \quad \forall n\in\mathbb{N}[/math]
we can assume that there is at least [math]a \in S_0[/math], and therefore that there is at least [math]a,N+a\in S_N[/math] but since this is true then also [math]a\in S_{N-k}[/math] for all valid [math]k[/math]
and then since I can choose any [math]N[/math], and there are an infinite amount of them this is true

i guess

>>10610494

exclusive or.

the smallest element of S_0 is the same, and the largest element increases by 1 from S_i to S_i+1. sequential values go away each step but reappear by trickling back up from the smallest. it's a weird problem.

>>10610538
>sequential values go away each step but reappear by trickling back up from the smallest
oof, could you elaborate more?

>>10610547

just start with 1234 and see what happens.

>>10610464
he's mad because he can't into latex

>>10610385
>the integer a is in Sn+1 if and only if exactly one of a−1 or a is in Sn
Does this mean that either a or a-1 can be in Sn, but not both (exclusive or)?

Pomf hi++ lol

>>10610986
based schizo

>>10611137
Yeah I'm schizoid so what

>>10611157
sorry, it's just very difficult to understand what you've written in >>10610986

>>10610893
well yeah what the fuck else would it mean?

>>10610986
nice

>>10611202
Lay off, I can’t tell you how many of these I’ve misread/misinterpreted

>>10610385
Yeah, I looked up the solution. There is no way in hell I would have figured this one out.

>>10611848
Where tf are the solutions?

>>10610464
OP has written entire post in [math] instead of only the math symbols that need to be in [math] to be readable.

>>10612457
kek

>>10612457

>>10610385 >>10612457
The feel when no autistic math nerd Touhou vampire waifu girlfriend.

Why even live?

https://www.youtube.com/watch?v=jTgYtkc4kgg

>>10610385
I thought i was being smart until i realised the problem asks for a proof where N is any integer, not just the positive ones
Am i trying to solve the general case now

>>10612581
I am*, fuck

>>10612581
S of n is only defined for n >= 0, so I think it’s safe to assume it means only the non-negative integers

>>10612581
Also, it doesn’t say any integer n, it just says infinitely many integers n

>>10612581
It seems like you don't even understand the problem. You have to such that there are infinitely many integers N such that S_N = ... holds. And it just so happens that S_N is only defined for positive integers N. Your proof is also missing the case that S_0 does not contain just 1 element.

>>10612581
It seems like you don't even understand the problem. You have to prove that there are infinitely many integers N such that S_N = ... holds. And it just so happens that S_N is only defined for positive integers N. Your proof is also missing the case that S_0 does not contain just 1 element

>>10612591
You don't know that, N could be negative and the definition of S of N would still be valid (adding negative number to a positive)
>>10612593
Then my proof is valid for when S0 consists of one element, now i jusy have to think of the general case

>>10612609
>You don't know that
Can you not read?
>N could be negative and the definition of S of N would still be valid (adding negative number to a positive)
The last line is not a definition of S_N. You really should work on your reading comprehension, it's very important for math.

>>10612616
You're the one that should work on your reading comprehension, because you seem to have misunderstood me. When i said that N could be negative and the definition would still be valid the definition i meant was the one in the original problem. My solution works only when N is positive and S0 consists of a single element, which is why i'm trying to find a general solution now (i.e. S0 has more than one element and N is any integer)
Either state exactly what i'm doing wrong or fuck off, don't be passive-aggressive. Are you saying my solution for this special case is wrong?

>>10612626
>When i said that N could be negative and the definition would still be valid the definition i meant was the one in the original problem.
That's exactly how I interpreted your post. I didn't look your solution. I was simply pointing out your misunderstanding of the problem.

>>10612626
It seems like you thought I thought you meant something else when I posted >>10612616, but what I thought you meant was exactly what you meant.

>>10612632
>>10612627
Explain what I am understanding wrong then. Is the case N=-3 for example not a valid one to consider? I understand that you have to prove that this is valid for infinitely many integers, not necessarily for all. I'm just curious exactly why you think my interpretation of N being possibly negative is wrong.

>>10612626
Looking at your proof of the special case now, it's also wrong. The part about S_n = {s, s+n} for all positive integer n is wrong.

>>10612635
The problem defines S_0 in the first sentence, then defines S_1, S_2, ... In the second sentence. Nowhere does it define S_{-3} or S of any negative integer.

>>10612636
Alright i am a fucking idiot, ignore everything i've said up till now (except the part where N can validly be negative)
For one element it seems S of 2^n equals {s, s+2^n}. It's possible i am once again talking out of my ass

>>10612638
>>10612591
>>10612593
>>10612609
>>10612616
>>10612626
>>10612627
>>10612632
>>10612635
>>10612636
>>10612648
I am a fucking muppet, i finally understood what you guys mean. S of N isn't defined independently, it's a progression from S0 and on and N obviously can't be negative because it's a fucking index. God i am such a brainlet. Please ignore everything i've said so far.
It does still seem that if S_0={s} S_2^n={s,s+2^n} but i am probably wrong about that as well. Jesus i am so retarded