Whole Numbers

Whole numbers are the complete set of counting numbers starting from zero, written as 0, 1, 2, 3, and continuing without end. They combine the natural numbers used to count real items with zero, which denotes nothingness and represents the absence of any quantity.

Natural numbers, successors, and predecessors

Natural numbers are the counting numbers that begin at one, such as when counting chairs in an office. Every number has a successor found by adding one, meaning even vast amounts like grains of sand or stars in the sky have a next number. A predecessor is the number that comes immediately before by subtracting one, making two the predecessor of three. Within natural numbers, the number one has no predecessor, but subtracting one from one reveals zero.

How zero creates whole numbers

• When four chairs stand in a room, counting them produces the natural number four.
• If all the chairs are removed and none remain, counting cannot begin with one.
• Zero gives a numerical value to this total absence of objects.
• Adding zero to the set of natural numbers completes the system, creating the whole numbers.
• Without zero acting as a distinct value, numbers cannot accurately show when an amount has emptied completely.

The ancient history of zero

• Around 4,000 years ago, Sumerians counted goats on cave walls and left an empty space for zero, but writing two space three made it easy to confuse 203 with 23.
• The Mayans later replaced the empty space with a specific symbol to mark the empty position, though they used it only as a placeholder rather than a true number.
• In 628 AD, an Indian mathematician named Brahmagupta became the first to define zero as an actual number, represented it with a dot below other numbers, and explained rules such as dividing by zero.
• Physical records of zero appear in the fifth-century Bakhshali Manuscript and in a ninth-century temple inscription located in Gwalior.