zDefs - (20) function a relation such that every element a...

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(1) least element (2) well-ordered – all subsets have a least element (3) principle of mathematical induction (4) minimum counterexample – in an induction proof, the assumption that if there is a counterexample, there is a minimal counterexample (5) relation – subset of AxB (6) domain – A first set in relation (7) codomain -- B (8) range – the set of second coordinates of f (9) reflexive – a R a (10) symmetric – a R b then b R a (11) transitive – a R b and b R c the a R c (12) equivalence relation – relation that is reflexive, transitive and symmetric (13) equivalence class – the set of all elements in A that are related to a (14) partition – collectively exhaustive, non empty, no element repeated in subsets (15) a|b – a divides b (16) congruence mod n -- (17) Division algorithm (18) Zn – integers modulo n (19) well-defined – sum or product of two equivalence classes does not depend on the representatives
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Unformatted text preview: (20) function a relation such that every element a in A is the first coordinate of exactly one ordered pair in f (21) image f(a) = b, b is the image/map of a (22) mapping (23) equality of functions (24) one-to-one every two distinct elements of A have distinct images in B (25) injective --every two distinct elements of A have distinct images in B (26) onto -- if every element of the codomain B is the image of some element of A (27) surjective if every element of the codomain B is the image of some element of A (28) bijective function that is both injective and subjective (29) identity function a function that maps an element to itself (30) composition function defined by g o f (a) = g(f(a)) (31) associative -- (32) inverse relation R^-1 = {(b,a): (a,b) e R} (33) permutation bijective function on A...
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