The Real Number System and Squares + Roots

Integer set

ℤ : { 0, +-1, +-2, +-3,…}

Integers

Positive and negative natural numbers, and zero

Rational Numbers set

ℚ : { a/b | a,b ∈ ℤ, b ≠ 0 }

Rational Numbers

Numbers that can be expressed as the quotient of two integers in the form a/b, where b ≠ 0.

Irrational Numbers definiton

Numbers that cannot be expressed as the quotient of two integers a/b, where b ≠ 0.

Irrational Numbers are…

decimal numbers that are non-repeating and non-terminating.

Natural numbers are…

another way of saying “counting numbers”

Natural Numbers set

ℕ : { 1, 2, 3, 4, … }

Whole Numbers set

𝕎 : { 0, 1, 2, 3, 4, … }

Prime numbers are

positive integers (n > 1) that have exactly two distinct divisors: 1 and itself.

Composite numbers are…

positive integers ( n > 1) that have more than 2 distinct divisors.

The set of real numbers is formed by…

the union of the sets of rational and irrational numbers.

Real Number set

ℝ : { ℚ ∪ ℚbar }

A square number / perfect square is the…

product of the same two numbers (integers).

A prime factorization is…

An expression of a positive integer as a product of its prime factors.

The positive square root of a number is called…

the principal square root.

A perfect cube is…

a number that can be written as a power with an integer base and exponent 3.