Whole Numbers – Adding Zero to the Count

Whole numbers are exactly the natural numbers with one addition: zero. The set is written {0, 1, 2, 3, 4, …}. It sounds like a small change, but adding zero to the number system took mathematicians thousands of years to fully accept – and it changed mathematics forever.

The Indian mathematician Brahmagupta was the first to treat zero as a number in its own right, with its own rules for arithmetic, in his 628 CE book Brahmasphutasiddhanta. Before this, many civilisations used a placeholder symbol for “nothing” in their number systems (the Babylonians and Maya both had placeholder zeros), but Brahmagupta was the first to say that zero could be added, subtracted, and multiplied just like any other number – a genuine conceptual leap. Ancient Greek mathematicians, by contrast, were famously uneasy with the idea of zero, since their philosophy of number was tied closely to counting physical, existing things – and “nothing” didn't seem like a real quantity to count at all.

What Are Whole Numbers?

Whole numbers are zero and all the positive counting numbers, with no fractions, decimals, or negative numbers: 0, 1, 2, 3, 4…

Is 0 a natural number or a whole number?

0 is not a natural number in most English-language curricula (natural numbers start at 1), but it is a whole number – whole numbers are defined precisely as “natural numbers plus zero.”

Why Zero Matters

Zero is essential as a placeholder in our place-value system (the difference between 5 and 50 is a zero) and as the additive identity – adding zero to any number leaves it unchanged, a property covered in detail later in this section.

Real-Life Application

Empty counts: zero items left in stock.
Starting points: a stopwatch starting at 0 seconds.
Temperature: 0°C, the freezing point of water.

Key Takeaways

Whole numbers are the natural numbers plus zero: {0, 1, 2, 3, …}.
Brahmagupta's 628 CE work was the first to give zero formal rules as a number.
Zero acts as a placeholder in place value and as the additive identity in arithmetic.

Practice: Whole Numbers

Is It a Whole Number?