Consider this definition of Well formed formulas in mathematical logic -
The set of all well formed formula is the smallest set of strings , WFF that satisfies
- All Boolean variables are in WFF, and so are the symbols Τ and F. We call such formulae atomic.
- If A and Β are any strings in WFF, then so are the strings (not A), (A and B), (A V β), (A —> β), (A = B)
Wouldn't there be exactly one such set of strings satisfying these properties of WFF ?
I don't understand the need for using the word smallest.