In what world does the entirety of the answer to one question take up the entire front and back of a notebook page
Man I did longer homework Friday evening. Had to write some proofs for my foundations of math homework (it's basically set theory): 5 or 6 problems, about 14-15 pages total.
How do you have proofs that long in a foundation of math class?
Hell if I know. I wish I could say it was just me being verbose but according to the professor it's actually happening for most people in the class. :/
EDIT - Not like it matters, I like writing proofs, but still. <_<
What are some of the things you are proving though?
Well I can't speak for the current homework assignment since that's not due until Wednesday (so that could definitely be me). We're mostly looking at various relations and proving whether they're equivalence relations, and if not which properties they do/don't satisfy. There was also one on partial order in there, and another one circular relations. Might be others that I forgot.
The previous one we haven't gotten back but everyone's stuff looked pretty long. I don't have the assignment in front of me but basically it was proving various properties of sets. Like (A union B) intersect C = (A union C) intersect (A union B). Stuff like that (that specific example might not be a property but it illustrates it essentially). There was also some stuff on fuzzy and crisp sets, and some quick set operation stuff (like you might be given a universe of discourse, a few sets, and you might find various unions, intersects, complements, stuff like that), though that didn't really take too long; same for a couple of problems in finding which sets were equivalent.
The previous one before that was proofs involving various properties of numbers. I recall proving:
- All rational numbers have a prime factorization, and that it's unique - That between any two rational numbers that there's an irrational, and an infinite number of them - We *might* have had to prove the opposite: between any two irrationals there's a rational, but I could be wrong - That "rounding" operations don't necessarily work with the distributive property (I didn't actually go into a full-blown proof on this: I was tempted but it quickly became a headache in my scratch work so I just went with a quick counterexample)
It's easy stuff - just takes some time I guess.
I just don't know how you are taking ~3 pages a proof at that level. But if your prof is fine with it, then it's whatever. ---
