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.

Infinity

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

The decimal expansion of 141120 will terminate after how many places?