I have the set:
B = {x ∈ {0,1}* | there is an equal number of 0's and 1's in x}
and therefore,
B* = {e,01,10,0011,0101,0110,1100,1010,1001,....etc}
I need to either prove or disprove that B*=B
I believe they are equal, because B* is just the concatenation of one string onto another. I think the trick is since the 0's and 1's have to be of equal number, that concatenating strings would keep the same number of 0's and 1's the same.
I just need a little help in the right direction as to prove B*=B. I was thinking of showing that if
B⊆B* and B*⊆B, that B*=B holds.
Any help would be much appreciated!