számkategóriák

Számkategóriák, or number categories, is a fundamental concept in mathematics referring to the classification of numbers based on their properties. These categories provide a framework for understanding the relationships and operations between different types of numbers.

The most basic category is the set of natural numbers, often denoted as N. These are the counting numbers: 1, 2, 3, and so on. Depending on the convention, natural numbers may also include zero.

Next are the integers, denoted by Z, which encompass natural numbers, their negative counterparts, and zero: ..., -3, -2, -1, 0, 1, 2, 3, ...

Rational numbers, represented by Q, are 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 and numbers with terminating or repeating decimal expansions.

The set of real numbers, denoted by R, includes all rational and irrational numbers. Irrational numbers, such as pi and the square root of 2, cannot be expressed as a simple fraction and have non-terminating, non-repeating decimal expansions.

Finally, complex numbers, denoted by C, extend the real number system by including the imaginary unit, i, where i^2 = -1. A complex number is generally written in the form a + bi, where a and b are real numbers. Each of these categories forms a subset of the next, creating a hierarchical structure that underpins mathematical analysis and computation.

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