Întregi

Întregi is the Romanian term used for the set of integers in mathematics. The plural form întregi appears when referring to numbers that are whole and without fractions, and it is commonly used in phrases like numere întregi (integers). The set of all integers is typically denoted by the symbol Z and can be written as Z = {..., -2, -1, 0, 1, 2, ...}. Integers include zero, positive integers, and negative integers.

The integers form a well-defined algebraic structure under the usual operations of addition and multiplication. They are closed under both operations, meaning that the result of adding or multiplying any two integers is again an integer. Every integer has an additive inverse (for example, the inverse of 7 is -7), which makes the set an abelian group under addition. With multiplication, the integers form a ring, and they have no zero divisors, so they constitute an integral domain. They are ordered in a natural way, providing a total order on the set.

Key properties include that division of integers does not always yield an integer; division is only exact when the dividend is a multiple of the divisor. Consequently, the integers are a subset of the rational, real, and complex number systems, but not all arithmetic operations among integers stay within the integers.

Usage in Romanian textbooks and discourse mirrors the mathematical concept: întregi refers to the whole-number values, and the term is paired with adjectives like numere întregi to emphasize their discrete, non-fractional nature. See also: număr întreg, setul Z, arithmetic.