Infinity

Infinity is thought of as an incalculably large number. In mathematics, it is not in the set of real numbers and so is not a number at all. An infinite answer to an equation is undefined. For example, dividing any number by zero results in infinity, so the answer is undefined. Even so, infinity is a useful concept in mathematics. Infinity is either positive infinity on the positive end or negative infinity at the negative end of the number system. Positive and negative infinity are used for defining set parameters of a function's domain and range. Some limit functions and summation functions examine results to equations as numbers approach infinity. There are infinite sets that represent different sizes of infinity, such as the set of real numbers and the set of integers. One way of comparing infinite sets is by showing a one to one correspondence between each of the set's elements. The term relative infinity describes a number that is so large that it might as well be infinity, compared with absolute infinity which is infinity itself. A finite number is any number that is not infinity.

The equation three divided by zero is equal to infinity, because it takes an infinite number to multiply times zero to reach three. Mathematics considers the answer to be undefined, since it is outside the set of real numbers. This set is normally the universal set used for answering all mathematical equation.

Math Mysteries: Infinity is necessary in mathematics. It is the true existential idea of mathematics. Important mathematical questions use the concept of infinity, even though it is basically incomprehensible due to the inherent nature of its size. Theoretically, in mathematics, there are an infinite number of different sizes of infinities. For example, there are an infinite number of integers and there are an infinite number of rational numbers between each one of those integers. Defining infinity is a mystery mathematics has yet to solve.