Whole Number
A whole number is any non-negative integer: 0, 1, 2, 3, and so on, with no fractions or decimals.
Definition
Whole numbers are the counting numbers plus zero: $0$, $1$, $2$, $3$, $4$, and so on, with no decimal point or fraction part, forming the set $W = \{0, 1, 2, 3, \ldots\}$. They differ from the natural numbers only in including $0$, and they are closed under addition and multiplication: adding or multiplying two whole numbers always produces another whole number. Formally, $W$ forms a commutative monoid under addition (identity $0$) and under multiplication (identity $1$), isomorphic to the non-negative part of $\mathbb{Z}$.
Example
You have $0$, $1$, $2$, or $3$ apples, and each of those counts is a whole number, but you cannot have $2.5$ apples as a whole number. $5 + 3 = 8$ and $4 \times 6 = 24$ stay whole numbers, but $3 - 5 = -2$ does not, so whole numbers are not closed under subtraction. The well-ordering principle states every non-empty subset of $W$ has a least element, a property that drives mathematical induction and the Euclidean algorithm.
Key Insight
Whole numbers are the numbers you use to count things in the real world, plus zero for "none at all." Every whole number is an integer, but negative integers like $-1$ and $-2$ are not whole numbers, so the whole numbers are a subset of the integers. Whether $0$ belongs to the "natural numbers" varies by convention: the ISO 80000-2 standard includes it, but many textbooks keep a separate "whole number" category to avoid ambiguity.