#mathblr

[bagalois]

abbreviates "with respect to" with wrt

"it is equivalent" instead of saying "it is the same"

"that's all one equivalence class of examples"

never says the word "normal" and opts for "general" "common" "usual" "typical" "canonical" instead

math-y sayings you can start using to have even less friends (= more time to study algebra):

"what the funct?"

"it's isomorphic" to mean "it's the same"

"ACR" (after certain rank) to mean "eventually"

"epsilonesque" to mean "very small"

"clopen door" to mean "half-open door"

abusing the prefix "co-" to invert the meaning of words

please reblog with more suggestions on how to become mathematically insufferable :>

[bagalois]

[michaelrotonal]

math update

41 is now prime, 91 is no longer prime

cubic triangular numbers larger than 1 have been removed

removed one sign so now there are only positive and negative numbers

klein bottle is no longer embeddable in 3-space

4 is now the smallest composite number rather than 3

cubes can now fit squares slightly larger than them

[jan-aki]

2 is such a victim of the strong law of small numbers cause it's somehow a (superior) highly COMPOSITE number despite being prime

[issnehaa]

For some weird reason, my dumbass is really attracted to guys who are good at math, like, ''Yes!! you know when to use which formula, that's so hottt''.

[spookyboogieanarchist]

Sat in advanced quantum mechanics class like:

[geometric-doofus]

mathblr give me one (1) book about math and I'll read it in full

[schrodingers-egg-yolk]

3 logicians walk into a bar to buy some beer. bartender asks "will you all be having beers then?"

the first says "I don't know"

the second says "I don't know"

the third says "yes"

An infinite number of mathematicians walk into a bar. The first orders 1 beer the second orders 2 beers the third orders 3 beers… the bartender stops them and says “you guys need to know your limits” and then steals 1/12 of a beer from them.

[lvl10blvkmage]

oh no , the dog is drinking the wave equation

[here-by-chance]

im obsessed

[sleepy-bebby]

[4denthusiast]

There are two rather different cases, depending on whether P=NP is in fact true. (Unlike, say, the continuum hypothesis, I don't think it would make much sense for P=NP to not have a determinate truth value. It can be expressed as a Σ_2 statement in Peano arithmetic.)

Suppose P≠NP but ZFC can't prove this. Then there is not actually any polynomial time SAT algorithm, but there are non-standard models of ZFC in which such algorithms do exist. I don't think these can be real algorithms, but there could be an algorithm in the model whose length is a non-standard natural. That wouldn't seem terribly weird to me.

In the other case, P=NP but ZFC can't prove this. This seems weirder, because there would be some specific algorithm A that solves SAT in polynomial time, but ZFC either can't prove it's correct or can't prove it's polynomial time. There would be some specific polynomial p too, which is a bound on the A's runtime. There is in fact a known algorithm which, by trying all possible other algorithms, is provably a polynomial time solution to SAT iff there is any such solution, and I think it is also provable that that particular algorithm does solve SAT, the only question is whether it's polynomial. We can therefore take A to be this particular algorithm wlog, therefore under the assumption that P=NP but ZFC can't prove this, ZFC in particular can't prove that A's runtime is bounded by p.

That I think would be very surprising. If an algorithm is polynomial, I feel intuitively that there's sort of a limit on how complex its state space can be, such that, even if the exact runtime bound can't be proven, it would be weird for there to be no proof of any polynomial bound. This is only a vague intuition and the formal statement in full generality ("All polynomial-time algorithms are provably polynomial-time.") isn't true, but I'd still be surprised by non-contrived counterexamples.

Out of all the Millennium problems, I think the one that would be funniest to be independent of ZFC would be P=NP

[h0bg0blin-meat]

Here's the link to the video

👏 SAY 👏 IT 👏 LOUDER 👏

[marigold-22]

They should make a new subject called dysfunctional analysis and I should be the only one allowed to teach it.

[michaelrotonal]

Customizable smooth transition function