So I have the absolute laziest Discrete Math professor in the history of professors who hands out homework that is 10x harder then anything in the lecture notes and includes steps not even covered there and then blows off questions/criticism from students with "It's good you are having a hard time with this, it's like the pain of lifting weights to get stronger"

So long story short I am just trying to pass this class and never have to take a math class again. I'm stuck on this, the last problem in the homework. I've got part 1 down but have no clue wtf to do on Part 2:

4) Prove the sets defined below are equal.

A = { (a, b) ∈ ℤ+ × ℤ+ | a is a factor of b }

B is defined recursively by
Initial Step: (1, 1) ∈ B
Recursive Step: [(a, b) ∈ B and k ∈ ℤ +] therefore [(ak, bk) ∈ B and (a, bk) ∈ B]

Overall strategy: To prove A = B, you must show A ⊆ B and B ⊆ A.
Part 1. To show A ⊆ B, prove the statement “If (r, s) ∈ A then (r, s) ∈ B.”
Begin with an arbitrary element of A, say (a, b) ∈ A. Then you must show (a, b) ∈
B. Hint: show how to use the recursive definition of B to build (a, b) (using the
recursive step finitely many times). Hint: Note that if (a, b) ∈ A, a and b are positive
integers such that a is a factor of b, and there is another integer k with ak = b.

Part 2. To show B ⊆ A, use structural induction to prove “If (r, s) ∈ B then (r, s) ∈ A.

have you done any recursive functions in your programming classes?

that brings back bad memories of the discrete math course I hated..
brain frying

i've written recursive functions, but i haven't found much use for them. wonder if i still have that book on fractal programming... bah, it'll make my head hurt... think it was mostly geared towards compression, of my brain.

Yeah I just put in some BS and turned in this assignment. This is going to be the longest 4 weeks of my life to get through this class. I absolutely hate it. One student stated he had 3 kids, worked full time, and was taking another programming class as well and he could not spend 10+ hours a week on a single homework assignment and her response to him was to just drop the class and take it when he had more time *eyeroll*

you want i should get drunk and call her a bunch of names?

sounds like she gets paid the same regardless no matter what. why i pay you to teach, if i have to go home and learn it all by myself?

YES IT"S MULTIPLICATION
IT"S MATH EDUCATION

recursion is fun, and i use it quite often when coding ... but it's been quite a while since i took discrete math .. and i remember that i never understood induction :( that fluff be strange :P

I remember this stuff enough to remember that I swore to forget it once I didn't need to use it to get a grade. :)

I feel for you man, that fluffs hurts peoples heads, no doubt.

recursion is really useful!

YOU CAN SOLVE MAZES USING RECURSION.
YOU CAN SORT USING RECURSION
BUT CAN YOU PROCREATE USING RECURSION??
:P

not entirely sure that i have the right equipment to engage in sexual recursion, let alone produce a child.

The issue wasnt recursion it was the structural induction stuff + recursion. :P

i feel old...i did those when i was still doing things like FA work :(