109 roundup

Definitions.
Quantifiers.
Proofs. Case check, contradiction, induction, series of reductions.
Make sure during induction that the chain of implications isn't broken anywhere.
To prove sets are equal, show both inclusions.
To prove functions are equal, check them on every element.
Functions; 1:1, onto, invertible.
Baby number theory. The division algorithm, Euclid's algorithm, the fact that the gcd can be written as an integer linear combination of the two numbers, unique factorization into primes. Congruences. Chinese Remainder Theorem.
Partitions and equivalence relations.
(n choose k) and the Pascal recurrence for it.