Number

Number – an abstract entity used to describe the amount. Sequence. There are different kinds of numbers. Natural numbers 1,2, used for counting objects. Set of natural numbers is denoted. If the natural numbers to add negative numbers and zero, we obtain integers.

Whole numbers in mathematics are studied within the framework of the theory of numbers. Relationships of integers are called rational numbers, or ordinary fractions. The set of all rational numbers is denoted. If by rational numbers add all the endless and non-recurring decimals are called irrational numbers, we get real numbers. Except unit on rational and irrational, real numbers are also classified into algebraic and transcendental. At the same time every transcendental number is irrational, every rational number – algebraic. Real numbers, in turn, can be extended to complex numbers. Complex numbers can be extended to quaternions, but multiplication of quaternions is noncommutative.

In turn, the octave are extensions of quaternions, are already losing the property of associativity. In mathematics, for the sets there is a set amount of power, a similar number of elements in it. The development of this submission for infinite sets led to a further generalization of the concept of number. Now talking about cardinal numbers, which describe the set of any number of elements – finite or infinite.