I am confused regarding the statements provided by one of our faculty regarding "Is it compulsory that every infinite set is non regular though every finite set is a regular set". Providing this example:
$$L= \{ 0^n 1^n | n>=0 \} $$ its formal as $\Sigma=\{0,1\}$ and thus we've a formal meaning as $\{\epsilon,01,0011,000111,....\}$
no. of 0's = no. of 1's
The above language should be a non-regular as we need to keep track the value of 'n' in order to make it a equal no, of 0's & 1's and FA has no memory.
or am i mistaken.
Please, provide some oxygen regarding this confusion.thank you.