Subject: Set-Theory Doubts: Got some conceptual glitches
Date: 12 Sep 1992 01:28:45 -0500
Organization: Kansas State University
Lines: 17
Message-ID: <18s2mtINN2gf@matt.ksu.ksu.edu>
NNTP-Posting-Host: matt.ksu.ksu.edu
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).
Would really appreciate if somebody helped clarify these concepts.
