proof

Question 1

how do you express an odd or even number

Answer 1

odd = 2n+1
even = 2n

Question 2

define natural number

Answer 2

positive integer from 1-infinity (also called counting numbers)

Question 3

define real number

Answer 3

number that can be expressed as an infinite decimal expansion
can be positive or negative

Question 4

how to express a positive real number

Answer 4

n^2

Question 5

how do you prove by contradiction

Answer 5

assume statement is wrong, through logical steps come to conclusion, deduce that first statement must be true

Question 6

how do you prove by deduction

Answer 6

start from known facts or definitions, use logical steps to reach conclusion.

Question 7

how do you prove identities

Answer 7

start with one expression of the identity, manipulate one side to match the other, showing steps

Question 8

how do you prove by exhaustion

Answer 8

break statement down into smaller cases, prove each case separately.