Numbers are among the most basic mathematical objects. They count objects, measure quantities, and label positions. The concept seems simple, but numbers come in many types: natural, integer, rational, irrational, real, complex.

Each extension of the number system solves problems the previous one could not. Natural numbers handle counting. Integers allow subtraction. Rational numbers allow division. Real numbers fill the gaps. Complex numbers solve equations like x² + 1 = 0.

Numbers have been represented in many ways: tally marks, Roman numerals, and place-value systems. The decimal system, with its base of ten, dominates today, though binary and hexadecimal are common in computing. Numbers are so fundamental that their study—number theory—is one of the oldest branches of mathematics.

• Used to count, measure, and label
• Types: natural, integer, rational, real, complex
• Each extension solves new problems
• Represented in various numeral systems