nombroj

Nombroj is the Esperanto word for numbers. In mathematics, nombroj are abstract objects used to count, measure, and label quantities. They appear in several closely related families, including natural numbers, integers, rational numbers, real numbers, and complex numbers. Each family extends the previous one by adding new elements and new properties.

Natural numbers are used for counting and begin with 0 or 1 depending on convention. Integers include negative numbers as well as the natural numbers. Rational numbers are ratios of integers, and real numbers include all rationals and irrationals such as sqrt(2) and pi. Complex numbers extend real numbers by including an imaginary unit i, allowing solutions to equations with no real solution.

Numbers are represented in numeral systems, the most common being decimal with base 10. Other bases such as binary (base 2) and hexadecimal (base 16) are used in computing. A number can have a finite decimal expansion (like 0.5) or an infinite one (like 1/3 = 0.333...). Some real numbers are irrational or transcendental, meaning they cannot be written as a fraction or as a root of a polynomial with rational coefficients.

Core operations on numbers include addition, subtraction, multiplication, division, and exponentiation. They satisfy properties such as associativity, commutativity, and distributivity, and obey ordering principles on the real and rational numbers. Number theory studies properties of integers, including primes, divisibility, and modular arithmetic, with applications in cryptography, coding, and computer science.

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