# The Definition of Limit

Let be a real valued function if the value of the function approaches a fixed number, say , as approaches a number, say . In this case we say that is the limit of function as approaches .

Mathematically, this can be written as:

We read it as “the limit of is as approaches ”.

If a variable assumes in succession a series of values

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