számok

Számok, the Hungarian term for numbers, are abstract mathematical objects used for counting, ordering, measuring, and describing quantities. They are commonly represented by numerals—symbols such as 0, 1, 2, and so on—within a chosen numeral system, with the decimal system being the most widespread in everyday use.

In mathematics, several classes of numbers are studied. Natural numbers N typically include the positive counting numbers, sometimes starting at 0. Integers Z extend natural numbers to negative values and zero. Rational numbers Q are fractions of integers. Real numbers R comprise all limits of convergent sequences, including rationals and irrational numbers that cannot be expressed as fractions. Complex numbers C consist of numbers of the form a + bi, where i is the imaginary unit.

Historically, many numeral systems have existed. The modern arithmetic foundation relies on the Hindu–Arabic decimal system, which uses place value and ten digits. Other bases, such as binary (base 2) and hexadecimal (base 16), are widely used in computing.

Operations and properties: Numbers support basic operations—addition, subtraction, multiplication, and division—along with order and equality relations. Zero serves as the additive identity; prime numbers are integers greater than 1 with exactly two positive divisors. Every integer can be expressed as a difference of two natural numbers; rationals are dense in the reals; irrationals have non-repeating, non-terminating decimal representations; complexes extend the real line by including imaginary components.

Applications: Numbers underpin mathematics and the sciences, providing foundations for measurement, statistics, and theory across disciplines, from number theory and algebra to geometry and analysis.