In a deposition submitted under oath, Relatif Tuinn said:
 RT>  RT>> Wrong. There are half as many even numbers as there are
 RT> integers.
 MB>  Can you prove this?  
 RT> Its a logical conclusion. The set of all even integers can never be as
 RT> big as the set of all integers. It has to be half by definition.
    It seems logical because our minds are used to dealing with finite
 numbers, and half of any finite number is smaller than the finite
 number.  But in dealing with infinity, things change.  Please see my
 post from March 21st wherein I show that:
 infinity + infinity = infinity = infinity ^ 2 = infinity ^ infinity, etc.
    If it has scrolled off your system, tell me and I'll repost the
 proof for you.
 MB>  practical purposes.  Here is the proof.
 MB> 1)  ((Infinity MOD 2) = 0)  = (0.5 * Infinity)  
 MB> 2)  (0.5 * Infinity) = Infinity, so also,
 MB> 3)  ((Infinity MOD 1) = 0)  = Infinity  ,
 MB> therefore:
 MB> 4)  ((Infinity MOD 2) = 0) minus ((Infinity MOD 1) = 0) = 0
 MB>  They are equivalent terms.
 RT> Infinity MOD 2 = 0 is only true if infinity is an even number. Is it?
 RT> If infinity is an odd number (which is equally possible) then Infinity
 RT> MOD 2 = 0.5
    Well, an odd number MOD 2 = 1, not 0.5, but you are correct in that
 his proof isn't valid as stated because the oddness or evenness of
 infinity is indeterminate.  If you have a very durable lamp and at noon
 every day you turn its switch to toggle it off or on, will it be on or
 off after an infinity of days?  You can never know.
    Again, I refer you and Mark to my post on infinity from the 21st to
 show the proof of what Mark was saying, that the infinite set of even
 integers is the same size (cardinality) as the infinite set of all
 integers, because both sets are countably infinite and both have a
 one-to-one correspondence to the set of all positive integers.
    This is what I mean, and maybe this is all the proof you'll need.
 In any case, it shows you what countably infinite means and gives a
 visual image of my proof to go with the one I referred you to.
    Positive Integers:  1  2  3  4  5  6  7  8  9  10  11  12  13  ...
         All Integers:  0  1 -1  2 -2  3 -3  4 -4   5  -5   6  -6  ...
        Even Integers:  0  2  4  6  8 10 12 14 16  18  20  22  24  ...
... There are three kinds of people; those who can count & those who can't.
--- PPoint 2.05
---------------