Hi
I am a new member. As per my understanding, if a variable in a formula does not fall under a quantifer, it is free and if it does, it is bound.
Could you tell me if my understanding correct?
I am currently reading the book "mathmatical logic for computer science" page 106. Please see the attached image or visit
Mathematical logic for computer science - Google Books
a proof has been given which mentions
A'= x A1(x)
and then the text: but x is the only free variable in A1 ...........
My question is: is x free? It falls under for all quantifier ...
Sorry for the long question and thank you for your help.
Suzzane.
This is correct; however, to be more precise, "free" or "bound" pertain to occurrences of variables. A variable can have both free and bound occurrences in a single formula. In this case, though, bound occurrences should be renamed for clarity.
See also this post for links about free and bound variables.