One-one: How about:
For all s, t in S: if s != t then f(s) != f(t).
(not sure what yours means, what's the w and the t?)
Alternatively:
For all s, t in S: if f(s) = f(t) then s = t.
Onto:
Yep, that seems okay to me.
I'm trying to write the definition of a one-one and onto functions using logical quantifiers. Is the following correct:
Let f be a function from S to W.
One-one:
If f(s) = w then for all s' in S such that s' != s, f(s') != t.
Onto:
For all w in W, there exists at least one s in S such that f(s) = w.
I'm pretty sure about what I've written for onto, but not about one-one. Thanks for helping me clarify these simple concepts.
Let:
(x) mean for all x
Ex mean there exists an x
E!x mean there exists a unique x
Let f:S------>W
And :
(f is one to one and onto) iff (w)[ wεW------>E!s( sεS & (s,w)εf)]........1
Now go into another thread in Miscellaneous to see the meaning of unique
Actually 1 straight away defines a function from W to S