How do you write that a number is an integer?

To denote that a number is an integer, you can express it in several ways, primarily depending on the context (mathematical notation, programming, or general writing). An integer, also known as a whole number, can be represented as n/1 and always ends before the decimal point. For example, 3 is an integer, because it can be written as 3/1.

Here's a breakdown of different methods:

Mathematical Notation

• Symbol ∈ ℤ: This is the most common and concise way. If you want to say that x is an integer, you would write:

  • x ∈ ℤ

  where ℤ (often typeset as Z) represents the set of all integers (..., -2, -1, 0, 1, 2, ...).

Formal Writing

• You can state it explicitly: "x is an integer."
• Alternatively, use phrases like:
  • "x is a whole number." (Though be mindful that some may interpret "whole number" to mean non-negative integers only).
  • "x is an element of the set of integers."

Programming

Different programming languages have different ways of declaring a variable as an integer:

• Example (Python):

x = 5  # x is implicitly an integer
print(type(x)) # Output: <class 'int'>

• Example (Java):

int x = 5; // x is explicitly declared as an integer
System.out.println(((Object)x).getClass().getSimpleName()); //Output: Integer

• Example (C++):

int x = 5; // x is explicitly declared as an integer

Examples Illustrating Integers and Non-Integers

Number	Is Integer?	Explanation
5	Yes	Can be represented as 5/1. Ends before the decimal point.
-3	Yes	Can be represented as -3/1. Negative whole numbers are also integers. Ends before the decimal point.
0	Yes	Can be represented as 0/1. Zero is an integer. Ends before the decimal point.
3.14	No	It's a decimal number. Its fractional representation is not n/1, rather it's a rational number (314/100).
7/2	No	Equals 3.5 which is a decimal number. Although a fraction, the denominator is not 1 after simplification.
10/5	Yes	Equals 2 which is an integer (2/1).