Infinity is an undefined number which can be negative and positive. A number is used as infinity sometimes, the sum of two numeric may be numeric but can be a different pattern, it may be negative or positive value.

It is used to compare solution in algorithms for best solution. Generally, a value set at the initial start may be positive or negative infinity, we have to take care that no input value is bigger or smaller.

**Infinity and Nan are two kinds of exceptional floating values in Python. **

**In comparison, positive infinity is always bigger ****than**** every natural number.**

(i.e. 0,1,2,.......... +∞. Positive integer and +infinity.)

**In comparison, negative infinity is smaller than ****negative**** number.**

(i.e. ∞-.......-2,-1,0, 1,.2,3......... – negative infinity and -integer.)

In python, we cannot represent infinity or we can say that there is no way to show the infinity as an integer. But we can use float (inf) as an integer.

**How to represent positive and negative infinity in Python:**

```
ptive_inf = float(“inf”) // for Positive infinity
ntive_inf = float(“-inf”) // for Negative infinity
```

**Infinity in Python 3.5 **

```
import math
test = math.inf
If we compare
ptive_inf > 1
ptive_inf > 1000000
```

It always true.

**Python Infinity and NaN (“not a number”)**

As we know that inf is infinity and is the undefined biggest number among positive numbers. When we try to subtract any number out of it then we get a “Not a number” (NaN). Even though infinity is the biggest integer but undefined, when something is undefined how can you subtract something from it, therefore, an error is NaN.

### NaN can be represented in Python using 3 basic ways:

**n= float ('-inf')**, for storing a negative infinite number

**p= float ('inf')**, for storing a positive infinity number

In Python 3 and higher, the NaN number is represented using the math.nan after importing the math module.

For example, **nan=math.nan **

This number can be evaluated using math.isnan(nan), where the nan is the argument passed to check whether it is NaN or not.

**Example**

```
ptive_inf = float (‘inf’) #positive infinity
ntive_inf = float(‘-inf’) #negative infinity
nann = float(‘nan) #Not a Number (NaN)
```

**math.inf in Python**

math.inf is a module in python, when we are talking about the infinity, it is assigned to a float variable with the help of **inf** as a float argument. This ‘**inf**’ constant is available with a math module. When we are dealing with the infinity we import math module.