MAS114 Revison Cards

Russell's Paradox: Prove that the set of all sets which are not elements of themselves is self-contradictory:

Two functions are equal if:

-Negation of A:
-Contra-positive of A⇒B:

Equivalence of:
¬(∀x ∈ X, P(x))
¬(∃x ∈ X s.t P(x))

Euclid's Theorem

Definitions:
-Greatest common divisor:
-Least common multiple:
-Co-prime:

gcd properties:

a ≡ b (mod m)

Congruence properties:

Fermat's little theorem

Fermat-Euler Theorem

Wilson's Theorem

x is irrational
y is rational

Convergence definition:

The four group axioms:

Albanian Group

(gh)^-1

Homomorphism:
Isomorphism:

Subgroup Criteria

Group Actions

Orbit Counting Theorem

Equivalence relations