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If a and b are integers, a divides b
if there exists an integer k so that b = ak
For a natural number n, n! =
n(n−1)(n−2)···3·2·1.
An integer n is even
if there exists an integer k so that it can be written as n = 2k
Two statements are equivalent
if their truth table match for all possible values of the component statements
Let a and b be integers. The greatest common divisor of a and b is denoted by gcd(a,b) and is the natural number d that satisfies the following two conditions
d divides both a and b. If n is an integer that divides both a and b then n divides d.
natural number definition
a counting number as in 1, 2, 3
whole number definition
a counting number or zero as in 0, 1, 2, 3
integer definition
a positive or negative counting number or zero
An integer n is odd
if there exists an integer k so that it can be written as n = 2k +1
mathematical statement definition
a declarative sentence which is either true or false.
negation definition
a statement having the opposite truth value of the original statement.
A conditional statement is
one of the form If P then Q
The converse of the conditional statement "If P, then Q" is
If Q, then P
The inverse of the conditional statement "If P, then Q" is
If not P, then not Q
The contrapositive of the conditional statement "If P, then Q" is
If not Q, then not P
A number n is a rational number if
it can be written as p/q for some integers p and q where q does not equal 0.
A natural number n is prime if
it has exactly two divisors namely 1 and itself
