>be me>math PhD candidate in Silicon Valley>interested in foundations>meet programmer>says he's interested in foundations too>show him Zorn's lemma>gets defensive>says that there need to be multiple maximal elements or something>write it off as him being dumb>meet another programmer>says he's also interested in foundations>wut, how?>show him Zorn's lemma>gets defensive>says something about stack ranking>wutWhy does this keep happening, /sci/? Are all programmers like this about foundations?
>>17011738((((Cantors))))) set theory killed math. Anybody should ridicoulate it. Actual infinity doesnt exist, only potential infinity.Thats why the axiom of choice has such controversial conclusions.
>>17011738eh, programers are more type/category theory kind of people than set theory, not to speak of intuitionism rather than classical logic
>>17011893>only potential infinity.potential within what?, time ain't infinite you retard, which mean that your potential infinity is as fictitious as set theory's actualized infinity
Because there is something appealing about foundations. It's making math more like programming. It's not less of a math if you don't care about it; enough people care for it to be relevant.
>>17011738Silicon valley
you are studying the most esoteric theoretical field in one of the most practical and money rich city in the country, maybe you are the dumb one
>>17012212I SEE YOU*Dr Evil expressing his love of mini me, Austin Powers*
the problem with zorn's lemma is it artificially constrains infinite sets with intuition. it can be used to prove 0.999... < 1.
>>17011958The concept of potential infinity doesn't need infinity. It just means it never stops, like a machine counting. It can go on and on, no boundaries. That's potential infinity.
>>17011738>future burger flipper living in theoryland trying to impress 6 figures engineers that actually build stuff
>>17011738Is this site just recycling posts from other sites now?
>>17011738>gets defensive about zorn's lemmaThe irony is thicc with this one. Have you ever tried to make an impassionate defense of intuitionism?
>>17011738programmers(engineers) are tier of intelligence below you. they cannot understand foundations because their intelligence operate off internalising a model.and normies cannot even internalise a model, they operate off simple universal heuristic rules.
>>17011738Never heard of zorn guy or his lemma until now, so, here is my review of it.zorn guy lemma is>if every chain in a partially ordered set X has an upper bound in X, then X contains at least one maximal elementThis guy is talking about sorting. Things are sorted, and he wants the maximum. Then he says "partially ordered set". What does that mean? Apparently, it means that two things don't have to be comparable. If things are not comparable, how can you sort it? Let's make up an example set. My set is A1,A2,A3,B1,B2,B3,and C1,C2,C3. A,B, and C, are different types and not directly comparable. In each chain, A chain, B chain, C, chain, 1 is small and 3 is big. The upper bound of A chain is obviously A3, the upper bound of B chain, is obviously B3, and the upper bound of C chain is obviously C3. Which is the maximum of A3, B3, and C3, which are not comparable?
>>17012819you gotta look up what a maximal element is, it's not the same as what you would consider a "maximum" when it comes to numbers
like take this anon >>17011893prime example of tier 4 mind. he needs to reframe any phenomenon within computation. typical engineer. i am myself mostly consciously sitting on tier 4, occasionally having tier 5 multisystem revelations. consequentially, i always had to put a lot of effort into math.
>>17012820Sure, and to continue with maximal element compared to maximum, the wikipedia has 2 examples. In the case of a set 1,2,3,4, you can make an element arbitrarily maximal by geometrically laying it out instead of evaluating it as an integer value. In the wikipedia example, the number 3 goes in the y direction while the others go in the x direction, so there are 2 maximal elements as the numbers are treated as points. Then there is a text example where being an additive string is maximal and being a unique string is maximal.
>>17012834So A3, B3 and C3 are all maximal elements and there is no problem. Your example doesn't deal with zorn's lemma's real implications since it is trivial on finite sets. That said it's important to get a feel for partial ordered sets since they are slightly unusual
>>17012542>It just means it never stopsand how the fuck can it do that if time ain't infinite you retard?
>>17012839Ok so if the A chain instead has 4 elements A1, A2, A3, and A4 and A4 is big, but A2 starts arguing that it is bigger than A3, then,If we disregard the C elements, say the minimum for a partially ordered set would be an A chain and a B chain, each chain having a minimum of 1 maximal element Amax and Bmax, then the minimum number of maximal elements should always be 2 or more for a partially ordered set
>>17012761>that actually build stuffI don't think zuck ever finished his gooniverseI don't think most engineers work more than 5 hours a week
>>17013047Those are two independent sets A and B to which the lemma applies so you end up with at least two. But for a general partially ordered set the lemma still says only 1. The core of zorn's lemma and why it is not obvious is that it's possible to create absolutely wild partially ordered sets, almost beyond imagination. In the case of finite sets it's indeed trivial just like any finite totally ordered set actually has a maximum by inspection.
>>17011738Silicon valley does the devils work. The world would be better if they sank into the sea. I will not help you.
>>17013291Do you know how gay this sounds?
