Question

If I have Σ={a} , what words does Σ* has ?

Σ*= {a,aa,aaa,aaaa.....} ?

Thanks

Answer 1

If your alphabet is Σ={a} then
Σ*= {#, a,aa,aaa,aaaa.....} means all the possible n* a, including the empty string # (phi). Another way to produce that sequence is using grammars:

S -> S
S -> aS
S -> #

where # is the empty string.