# Definition of Limit

Let $f\left( x \right)$ be a real valued function if the value of the function $f\left( x \right)$ approaches a fixed number say $L$ as $x$ approaches to a number say $a$, we say that $L$ is the limit of function $f\left( x \right)$ as $x$ approaches $a$.
Mathematical, it can be written in the form

We read it as “limit of $f$ is $L$ as $x$ approaches to $a$”.
If a variable $x$ assumes in succession a series of values

Then $x$ is becoming smaller and smaller as $n$ increases and can be made as small as we please by taking $n$ sufficiently large. This unending decrease of $x$ is mathematically written as $x \to 0$ and is read as $x$ tends to zero or $x$ approaches to zero.