Mathematical Symbols, Set Notation, and Number Intervals for Beginners

∀

For every

∃

There exists

∴

Therefore

∍

such that

∈

is a member of (or is an element of)

∉

is not a member of (or is not an element of)

∅ or { }

The Empty Set

x | x > 0

The set of all x values such that x is greater than zero.

The set of natural numbers {1, 2, 3, ...}

The set of integers {...,-3, -2, -1, 0, 1, 2, 3, ...}

+

The set of positive Integers {1, 2, 3, ...}

−

The set of negative integers {...,-3, -2, -1}

The set of rational numbers (ratios of integers; numbers which can be written as an integer divided by an integer)

I

The set of irrational numbers

The set of real numbers = ∪I

The set of complex numbers.

Closed Interval a,b

[ ] = x | a ≤ x ≤ b

Open Interval a,b

( ) = x | a < x < b

Half-Open (or Half-Closed) Interval [a,b)

= x | a ≤ x < b

Half-Open (or Half-Closed) Interval (a,b]

= x | a < x ≤ b

Infinite Interval

Always use an open interval (parentheses) with the infinity symbol.

= (−∞,∞)

Example of an infinite interval.

+ = [0,∞)

Example of an infinite interval.