I've only recently started learning this topic and I'm confused about these definitions:
I found two definitions for each type of variable which seemed to make sense:
Free variable 1: In mathematics, a free variable is a variable that specifies places in an expression where substitution may take place
Free variable 2: a variable, x, is free iff the variable does not occur in the scope of a quantifier.
Bound variable 1:A bound variable is a variable that was previously free, but has been bound to a specific value or set of values called domain of discourse or universe.
Bound variable 2: a variable, x, is bound iff the variable occurs in the scope of a quantifier.
I myself prefer the second definitions. However, there are examples where I cannot decide which type of variable I'm dealing with:
Based on the first definitions k should be a bound variable and n should be a free variable. But, based on the second ones, am I to say that they are of neither type, since a quantifier hasn't been used (If so, what kind of variable are they?)?