The Grammar of Mathematics, Volume 10

a₁ additive cancellation additive inverse algebra of sets algebra of statements analogues assertion atomic statements Axiom of pairing axioms basic laws binary relation binomial coefficient Boolean algebra called cancellation for addition cancellation properties chain ordering change-of-scope tautologies Chapter circuit commutative complex number compound statement conclusion condition consider constructed deduced defined disjunction element elementary equality equivalent example Exercise extension false finite follows given set Hasse diagram Hence identity implies induction inference interpretation least member logic Mathematical Induction mathematical proofs mathematics natural domain negation order relation pair partial order positive integer postulates premises problems proof prove PU Q quantifiers rational numbers real numbers represents require ring semiring set algebra set theory singleton statement algebra Suppose switches symbols tautologies Theorem tion triangles true truth tables U X V universe write