# Infinity

## What is Infinity?

Infinity is an idea of something that has no end. In general, it is something without any bound. It is a state of endlessness or having no limits in terms of time, space, or other quantity.

However, in mathematics, infinity is the conceptual expression of such a numberless number. It is often treated as if it were a number that counts or measures things: “an infinite number of terms, but it is not the same sort of number as natural or real numbers.

For example, A list of natural numbers 1, 2, 3, 4,…….no matter how long you count for, it can never reach the end of all numbers. Similar way, the never-ending universe, if you travel in the fastest spaceship, you can’t reach the end of an unending universe.

Meaning

A set of numbers can be defined as infinite if there exists a one-to-one correspondence between that set and a proper subset of itself.

Let us consider an example x+ 1 = x, this is only possible when x is an infinite number. The addition of 1 won’t result in the change on the original number.

Another way to represent infinite number is $\frac{1}{x}$, wehn $x\rightarrow 0$<

The infinity symbol ∞ is some time called the lemniscate and is a mathematical symbol representing the concept of infinity. The sign of infinity is used more often to represent a potential infinity, rather than to represent an actually infinite quantity such as the ordinal numbers and cardinal numbers. For instance, in the mathematical notation for summations and limits.

#### Practise This Question

If A and B are two square matrices such that B=A1 BA, then (A+B)2=