CMM: faq-proposed is a tag that anyone can edit in, but typically indicates that a post should at least be considered for the FAQ. Should we have a policy about when it is appropriate for users to edit in/what the appropriate usage should be?
you'd have to define that more formally; i'm not exactly sure what you mean by "coefficients that give the shortest vector" when there are multiple vectors in the solution basis
the main time i use scripts/programs for my homework is to run simulations to see if my answers for probability questions are correct (or look correct)
The way statistics is taught is always very unmathematical. It's probably because statistics is a useful subject and the actual math around it can be very complex, but I find it kind of a shame.
@GrainGhost I don't know if it's actually the case, but it felt to me like you just try a bunch of different ways to do stuff and see which works best (e.g. when determining outliers, you almost arbitrarily pick a number to be your threshold)
I'm okay with combinatorics and probability, though I don't like how there are often multiple ways of approaching the same problem and it's hard to know that I got the right answer. Statistics? Yeah, not my cup of tea.
@GrainGhost I absolutely hate stats. I love maths for the fact that, of all the things in this world, maths is probably the most objective. If someone can prove that some statement P is true, there's no disputing that, beyond disputing the absolute core of mathematics. Stats however contradicts this. You can make any set of numbers come to any conclusion you like with stats, which violates the beauty of maths for me
"When will we ever use this in real life?" "Shut up man, I want to apply this interesting technique to solve the problem, who cares about 'real life'?"
@hyper-neutrino @Anush I studied the problem and general mathematical solutions yesterday, and I'm inclined to believe that HN's method (even with division by GCD) doesn't give fully general solutions
@cairdcoinheringaahing Well, in actuallity you can choose your axioms how you want. Anything that's an axiom by one definition may be a theorem in another equivalent formulation. Bayes' law is sometimes an axiom sometimes a extremely simple result of other axioms, either way I think it's pretty silly to call it a theorem. Unless we are defining things in a rather contrived way (which sometimes happens).
Historically Bayes' law though is older than any sort of axiomatic treatment of statistics.
This is what happens when you bring up Bayes' law around me. I should come with a warning label about this.
@cairdcoinheringaahing ... Huh. I guess you can, if your sample space is uncountable (e.g. the real line or an interval on it). I think a partition of the real line can be defined as (or equivalent to) a set of real numbers representing the borders, in which case there doesn't seem to be a reason why that set has to be a countable set.
@DLosc Yeah, I was imagining a partition where each element in the partition is equal to a single real number in [0, 1]. That'd be uncountably infinite, and a disjoint partition, but I can't think of a "scenario" where that'd be the actual sample space
Probably depends on exactly what is meant by "parition", when we talk about paritions for e.g. integral definitions I'm pretty sure it's understood to be locally finite. Which sort of rules out uncountable.
Ah yeah there it just means some class of disjoint covering subsets, so yeah if your set is uncountable you can have that by just putting each point in it's own subset.
Otherwise you are going to have trouble even evaluating the summation there.
I mean there's already some issues with having to evaluate countable sums.
@hyper-neutrino That doesn't make much sense. It could be considered unreasonable for PyGamer to not study humans, in which case it could also be unreasonable for you not to study particles. Besides, particles are very different from humans, and society's expectations for the two differ a lot. It's very much a double standard and one of the many things wrong with our society
Societal expectations for particles are pretty tough...I hear neutrons are under so much societal pressure to stay neutral all the time they can just randomly tear themselves apart.
And there's always the threat of antiparticles deciding to annihilate you
@RedwolfPrograms Yes, fortunately those never get older
@RedwolfPrograms But they're the enemy! Electrons may be negative but they can't help it, and they're one of us. Positrons are anti-everything we stand for