Given any language L which is a subset of {0,1}* define the language unary(L) = { 0[sup]1x[/sup] | x is a member of L} The language unary(L) is said to be unary since it is a subset of 0 For instance, if L = {0, 1, 11, 000} then unary(L) = {00, 000, 0000000, 00000000}. Show that L is recursive if and only if unary(L) is recursive.

what i am trying to do at the moment is trying to use closure properties of recursive languages to transform any language into unary(L) of that language. I have a strong feeling after trying this for a few hours that i am on the wrong path. Can anyone give a hint please?

I also think that i dont fully understand what it means for a language to be recursive. If anyone could help explain that I would appreciate it!