In article <18s2mtINN2gf@matt.ksu.ksu.edu> bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
>a) According to my textbook, the ORDERED PAIR of two objects x and y is the set <x,y> = {{x}, {x,y}}.
>What throws me off is the definition; what is the motivation behind it?
Don't take these definitions too seriously. This definition is there
purely to formalize the definitions in terms of a basic set of set
theoretic axioms. But most mathematicians, once they are satisfied that
an ordered pair can be formalized, stop paying much attention to this
definition, and think of ordered pairs in intuitive terms.
>b) Let f: X --> Y be an injective mapping. By definition, this means:
> for all x, x' in X: f(x) = f(x') ==> x=x'.
>My question here is: for the firstmentioned implication why is the CONVERSE not true? (I know it's not but am having trouble finding an intuitive/logical answerfor it).
I assume that by CONVERSE you mean that x=x' ==> f(x) = f(x'). This is
certainly true. It is implicit in the definition of a mapping, so is
