Lecture 7 - Integer Properties (Part 1)

Vocabulary flashcards covering key concepts from a lecture on Integer Properties, including definitions of even/odd integers, divisibility, the division algorithm, number systems, prime/composite numbers, and rational numbers.

Even integer

An integer n is even if there is an integer k such that n = 2k.

Odd integer

An integer n is odd if there is an integer k such that n = 2k+1.

d divides n (d | n)

Let d and n be two integers and d \u2260 0. d divides n if there is an integer k such that n = kd.

Multiple

If d divides n, then n is said to be a multiple of d.

Divisor (or Factor)

If d divides n, then d is a divisor (or factor) of n.

Division Algorithm

For an integer n and a positive integer d, there are unique integers q (quotient) and r (remainder) such that n = qd + r, where r {0, 1, 2, …, d-1}.

Quotient (q)

In the Division Algorithm (n = qd + r), q is the quotient, calculated as q = n div d = round down (n / d).

Remainder (r)

In the Division Algorithm (n = qd + r), r is the remainder, calculated as r = n mod d = n

qd, and r {0, 1, 2, …, d-1} .

Number system

Each number system has a base and a set of digits that can be used to represent numbers.

Decimal number system

A number system with a base of 10 that uses 10 digits: 0-9.

Binary system

A number system with a base of 2 that uses digits 0 and 1.

Hexadecimal system

A number system with a base of 16 that uses digits 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15).

Prime number

An integer n is prime if it is greater than 1 and its only factors are 1 and itself.

Composite number

An integer n is composite if and only if n > 1, and there is an integer m such that 1 < m < n and m | n.

Inequalities

Mathematical statements comparing values, such as x < c (less than), x = c (equal to), or x > c (greater than).

Greater than or equal to (x

c)

A comparison where x is either larger than c or exactly equal to c.

Less than or equal to (x

c)

A comparison where x is either smaller than c or exactly equal to c.

Rational number

A number x is rational if there exist integers a and b such that b

0 and x = a/b.