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abelian accumulation point algebraic structure Assign a grade Assume Axiom of Choice Bolzano-Weierstrass Theorem cardinal number Claim codomain conditional sentence contradiction contrapositive converse countable countable sets cyclic group defined Definition Let denumerable digraph direct proof divides domain equivalence class equivalence relation exercise exists F F F F failure F T F false family of sets Figure finite set G o F Give an example given graph Heine-Borel Theorem Hint iff x e implies induction infinite set integer inverse irrational isomorphic Justify assignments Let G mathematics natural number normal subgroup number of elements one-to-one correspondence ordered field ordered pairs partially correct partition permutation prime Proofs to Grade properties propositional forms quantifier rational numbers real number reflexive sequence statement subgroup of G symbol symmetric tautology transitive true truth table upper bound vertex vertices