linear algebra and intro to proofs

implication

a statement in the form “if A then B” where A and B are statements or phrases. either true or false, never both

hypothesis, condition

the A part of an implication

conclusion

the B part of an implication

counterexample

for an implication, an example where the hypothesis is true but the conclusion is false

converse

“If A then B” has the converse “If B then A”

contrapositive

“If A then B” has the contrapositive “if not B then not A”

quantifiers

“for all x” or “there exists x such that”

set

an unordered collection of elements without repeated elements

cardinality

the number of elements that a set contains

subsets

if A and B are sets, and every element of A is an element of B, then A is a subset of B

set equality

A and B are equal if and only if A is a subset of B and B is a subset of A

Z with bar

set of integers (positive and negative whole numbers, including zero)

R with bar

set of real numbers

Q with bar

set of rational numbers (numbers in the form p/q where p, q are integers and q does not equal zero)