BS>ME>AC>half infinite line.  That's illogical and undefined.
BS>ME>The infinite anything is already illogical and undefined if thought of
BS>ME>as an actuality instead of as a potential.
BS>   It is not necessarily undefined, but can be defined in many ways.
BS>And infinity is anything *but* illogical.
Logic is the art of noncontradictory identification.  To speak of the
"infinite" is to speak of something beyond measurement.  Measurement is
the relation or effect of one thing to or upon others.  If something
cannot be measured it has no relation and no effect to or on anything
else, which is another way of saying it does not exist.  To claim
something exists which does not exist is quite illogical.
BS>   One (informal) definition of the infinity of positive real numbers
BS>is that for any and every very large number M you can name, I can
BS>always name larger numbers, such as M + 1, or M + M, or M * M, or M ^ M
BS>(M to the power of M).  A definition of negative infinity is similar,
BS>in that for any and every very negative number N of large magnitude you
BS>can name, I can always name one with a larger negative magnitude, e.g.,
BS>N - 1, N + N, N * -N, etc.
Your own definition, if you care to examine it, contains my argument:
"I can always name larger numbers". But any actual number you name is
always a finite one, no matter how large it is. No matter how long we
play the bigger number game, the actual named number remains finite.
The infinite is in the potential of the series to go on beyond
wherever we come to rest on the number line, but wherever we come to
rest is always finite.
BS>    And just to potentially blow your mind, the infinite set of all
BS> integers is larger than the infinite set of positive integers, which is
BS> larger than the infinite set of all even, positive integers, which is
BS> larger than the infinite set of all positive integers evenly divisible
BS> by 3, which is larger than... well, perhaps you get the picture.
Actually, it was an examination of this problem by a math professor of
mine at VA Tech which got me looking at infinity seriously for the
first time.  He was able to show that multiples of infinities are not
larger than one another.  IOW, he showed us a mathematical proof
that showed there would be "just as many" even integers (2,4,6...) as
there are single integers (1,2,3...).  Both infinities were identical
in the nature of the set.
BS>    May I recommend _Infinity and the Mind_ by Rudy Rucker, in paperback
BS> by Bantam Books, ISBN 0-553-23433-1.  Fascinating book on the "science
BS> and philosophy of the infinite."
I recommend you examine the term "infinite" for logical flaws in the
concept itself.  You will find that Mr. Rucker's title, if not his
argument, is quite well stated "_Infinity and the Mind_", but better
stated "_Infinity in the Mind_".
      As ever,
                 Matt Eggleston
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