TOC epsilon closure doubt

Question

Please explain? 

Answer 1

Following the definition of Kleene's closure and positive closure , we have :

a) ϵ⁺  =  { ϵ ,  ϵ .ϵ , ........... }  =  { ϵ }

b) ϵ*  = {  ϵ⁰ , ϵ , ϵ .ϵ , ......... } =  { ϵ } 

So we can conclude : 

 ϵ+  =   ϵ* 

In fact the statement : 

r⁺  =  r*  -  { ϵ } is true only if  { ϵ }  is not a part of r⁺ ..Else it is false as in the case above..

Comments

Okay Thanks !!!