/sci/ - Science & Math

>>12180270
Okay, thanks, I get a feel for it now. Hopefully I'll not forget it too soon, though.
But still, it feels like there's some vague tie to ideas. Especially in how the cofinality of [math]\aleph_\delta[/math] jumps between big and small when you're on a successor vs. a limit in the the ordinal. Although I don't really know what ordinals are between such alepha.

>>12180306
27:15 - 31:15
is fun to watch

>>12181337
There's nothing wrong with working explicitly without the excluded middle, I don't know why this is so misunderstood.

Let [math]{\mathbb N}^{\mathbb N} [/math] be the functions on the naturals.
Let [math]P \subset {\mathbb N}^{\mathbb N} [/math] be the functions that can be coded up (in C++, say).
Let [math]C \subset P [/math] be the functions that, on the inputs 0 say, are total / terminating / computable (excludes e.g. infinite while-loops).
Let [math]e \colon {\mathbb N}\to P [/math] be an enumeration of all codes.
Let [math]I_C := \{i\in {\mathbb N}\mid e(i)\ {\text {is computable} } \} [/math] be the index set of terminating functions.

The property of termination is not decidable, i.e. provably there’s no algorithm that you could give any C++ code so that it tells you whether it would terminate
So [math]I_C [/math] cannot be decidable either.
As a result, there is no computable surjection
[math]{\mathbb N}\to I_C [/math].
As a result, there is no computable surjection
[math]{\mathbb N}\to C [/math].

If you want to logically reason about this scenario, then you must tune your logic to respect this situation.

LEM plus a few set theory axioms imply that any infinite subsets of the nats is in bijection with it, but this is misleading. If ZF proves some set is "countable", then this word just means a formal existence statement
[math]\exists f. \dots[/math]
It's similar to a choice principle.To claim that every infinite subset of the naturals is "countable" is merely to adopt this as an axiom. Not that there's anything wrong with it.

The global AI drive will run parallelly simulate Kripke models relevant for optimizing star-energy exhaustion in a paraconsistent univalent Martin-Löf type theory within the Effective topos. And the universe will be increasingly be drained of any and all fluctuation.

>>11771917
sure

what happens in the first episode again? someone an hero and Lain tries to talk with her dad?
Anyway, sure do

>>11581403
>0/36/72-35/71/99
I like the effort you put into this

>>11581409
Just don't respond. It should be obvious that the person who did the lengthly anti-LEM shilling (me) isn't the same person as all the faggot talk (>inb4 why the homophobia)

>>11581410
There's a lot of syllogism
https://en.wikipedia.org/wiki/Syllogism
and many will be derivable in various systems.
Maybe this helps (also just one system)
https://en.wikipedia.org/wiki/Natural_deduction

>>11554991
*societies ethical values

Unless you think society is an acting entity in a Idealist kind of sense