Real numbers include every point on the number line. They encompass natural numbers, integers, rational numbers, and irrational numbers. Pi, √2, 0.5, −7, and 1,000,000 are all real. The set is denoted by R.

Real numbers are ordered: for any two, one is greater or less. They are complete: there are no gaps. That completeness makes calculus possible. Limits, continuity, and derivatives all rely on the real number system.

Real numbers can be represented as decimals, though irrational ones require infinite non-repeating expansions. In computation, real numbers are approximated by floating-point values with limited precision. The distinction between exact real numbers and their approximations matters in numerical analysis.

• All points on the continuous number line
• Includes rational and irrational numbers
• Ordered and complete
• Foundation of calculus