Re: Is continuum completely filled up?


"Dave Seaman" <dseaman@xxxxxxxxxxxx> wrote in message
news:er262c$a15$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Exactly what is there about the axiom of infinity that you want to
discuss?

Thank you continuing feedback to my trifling question.
It is difficult for me to answer to your question at once, because already
I have shown my opinion, nevertheless you agree non of them. As for
these problems, various people have argued at vaious places so far, so
much.
I am learning from you rather than discussing. My opinion might change
some day, but I would develop my idea until that day. I would like to
study and answer you little by little.
I want to show my axiom system, interplitation of traditional theory and
proof.
At first I accept finite set, but interplit infinite set in different
meaning.
Probably it may be main to ristrict traditional use of concepts. I accept
infinite collection of natural number and real line. Because naturals are
not finite and never ending one to one correspondence between natural
numbers and even numbers actually exist.
Nevertheless I can't know all of its members. Perhaps once pi is defined,
its infinite decimal expantion exist at the same time. But I cannot only
know all its digits, but also can not understand its meaning of existence.
Only I can say is that they are endless, so that I take this statement
as difinition of infinite set. That is, all infinite set is countable.
I know from wikipedia that in constructive thheory also, countability of
reals cannot necessarily be derived. But what I regard most important
is not constructivty of proof, but countability of objects.

Regards
Ozaki Toshiaki



.

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