Subject: Re: Set-Theory Doubts: Got some conceptual glitches
Date: 12 Sep 1992 19:41:50 -0500
Organization: Kansas State University
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Message-ID: <18u2oeINNndt@matt.ksu.ksu.edu>
References: <18s2mtINN2gf@matt.ksu.ksu.edu>
NNTP-Posting-Host: matt.ksu.ksu.edu
bubai@matt.ksu.ksu.edu (P.Chatterjee) writes:
>Hello there,
>I was just wondering if somebody on the net could help clarify a few conceptual glitches I have regarding very elementary concepts of set-theory.
>a) According to my textbook, the ORDERED PAIR of two objects x and y is the set <x,y> = {{x}, {x,y}}. It also goes on to state that by this definition, the ordered pair is determined by x and y; and the order, x first and y second, is important unless x=y.
>What throws me off is the definition; what is the motivation behind it?
>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'.
>Equivalently, x not equal to x' ==> f(x) not equal to f(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'm sorry for the STUPID statement about the CONVERSE being untrue; of course, by the definition of a function, as some people pointed out, the converse is true. Obviously, I got caught up in the 'logical' bind of 'if P, then Q' propositions and made the error of thoughtlessly discounting the reverse implication.
Anyway, thanks to all concerned who pointed it out.
>Would really appreciate if somebody helped clarify these concepts.
