Integers

Integer Definition:

An integer is a positive or negative whole number (including 0). This cannot be a fraction.

Integer Notation

We represent the set of integers as ℤ
Integers extend from but do not include (-∞, ∞)

What do Integers Include?

Natural (Counting) Numbers (ℕ) (1, 2, 3, 4, ...)
Whole Numbers (0, 1, 2, 3, 4, ...)
Negative Counting Numbers (..., -4, -3, -2, -1)

What do Integers NOT Include?

Rational Numbers (ℚ) (Fractions, Decimals) (1/2, 0.8, 3.5, ... )
Irrational Numbers (like π, Euler's Number (e) = 2.718281828459, √2, etc)
Positive Infinity ∞
Negative Infinity -∞
Imaginary Numbers like i = √-1

Properties of Integers

Positive integers are to the right of 0 on a number line
Negative integers are to the left of 0 on a number line
As we move right on the number line, integers increase in value
As we move left on the number line, integers decrease in value
Extend infinitely (but do not include infinity)
Any non-zero integer is either negative or positive.

Properties of Integers:

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Integers Calculator:

Integer Check

How does the Integers Calculator work?

Free Integers Calculator - This lesson walks you through what integers are, how to write integers, integer notation, and what‘s included in integers

What 1 formula is used for the Integers Calculator?

ℤ → (-∞, ∞)

For more math formulas, check out our Formula Dossier

What 5 concepts are covered in the Integers Calculator?

integers
natural number: the positive integers (whole numbers)
1, 2, 3, ...
number: an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification. A quantity or amount.
property: an attribute, quality, or characteristic of something
whole: numbers that include natural numbers and zero