Számkészletekre

Számkészletekre, also known as number sets, are fundamental concepts in mathematics. They are collections of numbers that share specific properties. The most basic and commonly encountered number set is the set of natural numbers, which typically includes positive integers starting from 1 (1, 2, 3, ...). Some definitions also include 0 in the set of natural numbers.

Expanding upon natural numbers, we have the set of whole numbers, which comprises all natural numbers and zero (0, 1, 2, 3, ...). The integers encompass all whole numbers and their negative counterparts (-3, -2, -1, 0, 1, 2, 3, ...). This set is denoted by the symbol Z.

The set of rational numbers, denoted by Q, includes all numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero. This includes all integers, as any integer n can be written as n/1. Examples of rational numbers are 1/2, -3/4, and 5.

Real numbers, represented by R, encompass all rational and irrational numbers. Irrational numbers are numbers that cannot be expressed as a simple fraction, such as pi (π) and the square root of 2. The set of real numbers forms a continuous line, often referred to as the number line.

Beyond these, mathematicians also work with complex numbers, which extend the real number system by including the imaginary unit 'i', where i² = -1. Complex numbers are expressed in the form a + bi, where a and b are real numbers. These various number sets provide a structured framework for solving a wide range of mathematical problems.