Infinity (symbolically represented by **∞**) is a concept in mathematics and philosophy that refers to a quantity without bound or end
.The word infinity comes from the Latin word infinitas which means unclear.

It counts or measures things or an infinite number of terms but it’s not the same sort of number as the real numbers .The set of integers are countably infinite, while the set of real numbers are uncountably infinite .The symbol for infinity looks like ribbon( `oo` ).

Most of mathematics that deals with the infinite that can also be interpreted as dealing with the potentially infinite number. Let us take an example, the question of whether any of a species will have an infinite chain of descendant species can be defined in such a way that requires quantification over all those reals . There occurs not a single event that decides this question but it is still meaningful and it is also interesting in a potentially infinite universe. It can be determined by a recursively enumerable set of events that are listed by a computer. In mathematics the inverse of infinity leads to zero.

**Limits to infinity:**

There includes limits of the functions where it approaches as x tends to infinity. Here L' Hopital's Rule is mostly used. If we try these problems before looking at the solutions, we can avoid common mistakes.

So the correct forms are `oo` / `oo` is not equal to one and `oo` -`oo ` is not equal to 0. Using algebraic manipulation we can circumvent these indeterminate forms. The following problems need the algebraic computation of limits of functions as x approaches plus or minus infinity.

**Example 1:**

** ** Compute the following `lim_(x->oo)` ** **
100/x^{2}+5** ** ..

** Solution:**

** **100/x^{2}+5 where x tends to
infinity.

**
=** ** **100/`oo` ^{2}+5.

= 100/`oo`

Here the numerator is 100 and the denominator is infinity.

Any numerical number which divides the infinity equals
0.** **

So the answer is **0.**

**Example 2:**

** ** Compute the following `lim_(x->oo)`** **
3x^{3}-1000x^{2} ** ** .

**Solution:**

3x^{3}-1000x^{2} ** **where x tends to infinity.

= 3(`oo` )^{3}-1000(`oo` )^{2}.

= `oo` -`oo`

= `oo ` and `!=` 0.

This is not equal to 0.This is an indeterminate for. By factoring it can be curmvented.

**Problem 1:**

** ** Compute the following `lim_(x->oo)` x+5/3x+7 <br>

** Solution:** The answer is `oo`

**Problem 2:**

** ** Compute the following `lim_(x->oo)`
x^{5}-x^{2}+x-4** **

** ** **Solution:** The answer is `oo` ** ** .

**Problem 3:**

** ** Compute the following `lim_(x->oo)` 5x^{2}-x+45/4-x

** Solution:** The answer is `oo`