Foundations of Computing: Proofs and Mathematical Logic

These flashcards cover essential vocabulary related to proofs, prime numbers, implications, and types of mathematical progressions from the lecture.

Proof

A statement that establishes the correctness of a mathematical statement through logical reasoning.

Prime number

A natural number greater than 1 that has no positive divisors other than 1 and itself.

Counterexample

An example that disproves a statement or proposition.

Implication

A logical statement of the form 'If A, then B', indicating that if A is true, then B must also be true.

Even number

A natural number n is called even if n can be expressed as n = 2k for some integer k.

Odd number

A natural number n is called odd if n can be expressed as n = 2k + 1 for some integer k.

Arithmetic progression

A sequence of numbers in which the difference between consecutive terms is constant.

Geometric progression

A sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio.

Mathematical induction

A method of proof used to establish that a statement is true for all natural numbers.

Straightforward proof

A proof that shows the equality of two sides of an equation directly by manipulating the expressions.