Self Doubt TOC Enumeration Method

Question

If language L is countable infinite set then,

 L is Recursive as we can define enumeration method for the countable set.

or It can Regular ??

Answer 1

Regular language is able to do only finite counting,infinite counting is not possible in regular language

eg-    L={a^n b^n  |n>=1}

         L={ab,aabb,aaabbb,aaaabbbb.........} , this is infinite language where equal no. of a's and b's.

      we can derive the enumeration procedure for this language but it is not a regular language

Answer 2

For L={a^n b^n  |n>=0} we can have the enumeration procedure but it is not a regular language