Power of Sigma (Σ) in TOC

Sigma (Σ) is a set of symbols used in a language. Sigma (Σ) represent the alphabet. It is denoted with Σ. The minimum power of sigma (Σ) is zero.

Formula

Hare Formula of Sigma are as follows.

Explanation: Where K tells about total number of sigma values and N tells about maximum length of the string.

Examples 

We can easily understand the examples by helping the Σ = {a, b}

Sigma with Power Zero (K=2, N=0)

Σ⁰ = Σ⁰ = 2⁰ = 1

It means that set of strings with the length is zero, Now lets solve the example.

The answer of this example length is epsilon {ε}. It is also known as null string.

Sigma with Power One (K=2, N=1)

Σ(a, b)¹ = Σ¹ = 2¹ = 2

It means that set of strings with the length is one, Now lets solve the example.

The answer of this example  length is {a, b}.

Sigma with Power Two (K=2, N=2)

Σ(a, b)² = Σ² = 2² = 4

It means that set of strings with the length is two, Now lets solve the example.

The answer of this example length is {aa, ab, ba, bb}.

Sigma with Power Three (K=2, N=3)

Σ(a, b)³= Σ³= 2³ = 8

It means that set of strings with the length is three, Now lets solve the example.

The answer of this example length is {aaa, aab, aba, abb, baa, bab, bba, bbb}.

Sigma with Power Σ* (Kleene Closure)

(a+b)* = Infinite Language

Set of all strings of all length possible of a and b.

It is set of all strings of all length possible of a and b known as a Kleene Closure.