READING:     I     4     5                    Back to reading:     I     4     4
begin quote ita"
CHAPTER I [:] Notions from Set Theory [...] 4. FINITE AND INFINITE SETS. "end quote
These pages assume that the reader has the book and is reading along.    
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Please read these notes from the beginning to here and then the remainder of paragraph 4 of 4 (after the previous two readings).

PROPER SUBSETS OF INFINITE SETS (continued)

Rosenlicht continues:

begin quote ita-1-4-4-pg11 "
[...] On the other hand, if   X   is infinite then [see reading I 4 2] there exist distinct elements   x, x, x,...   in   x.   The compliment of   { x, x, x,... }   in   X   is a subset   Y,   so that


X   =   { x, x, x,... } Y        and        { x, x, x,... } Y   =   .

A one-one correspondence between   X   and its proper subset   { x, x,... } Y   is given by the function which sends each   x   into   x   and each element of   Y   into itself.   This proves the "only if" part, completing the proof.
"end quote

on to reading 6