täisarvul

Täisarvul (from Estonian "täisarv," meaning "integer") refers to integer numbers in mathematics. Integers are a set of numbers that include all positive whole numbers, their negative counterparts, and zero. The set of integers is commonly denoted by the symbol Z, originating from the German word "Zahlen," meaning "numbers."

Integers are fundamental in various branches of mathematics, serving as the basis for arithmetic operations such as addition, subtraction, multiplication, and division (except division by zero). They are used to represent countable quantities, position, and to express concepts such as parity, divisibility, and congruence. The properties of integers underpin many areas including number theory, algebra, and computer science.

The set of integers can be formally defined as the union of natural numbers (positive whole numbers), zero, and negative natural numbers. The set is closed under addition and subtraction, meaning the result of these operations on any two integers is always an integer. However, division of two integers does not necessarily result in an integer unless the divisor divides the dividend evenly.

Integers are visualized on the number line, extending infinitely in both directions. They are essential for understanding more complex numerical systems, such as rational numbers, real numbers, and complex numbers. In practical applications, integers are used for indexing, counting, and discrete mathematics problems.

Overall, täisarvul is an integral concept in mathematics, providing foundational knowledge vital for both theoretical and applied sciences.