Re: Galileo's Paradox and the Project of the Reals

Mike Kelly wrote:
Tony Orlow wrote:
David Marcus wrote:
Tony Orlow wrote:
David Marcus wrote:
You haven't noticed that Tony is a crank? And, that what he wrote above
is vague nonsense?
I'd rather be a crank than a cog, or a stick in the mud, David.
Then I guess you've got your wish. Tell me: are you incapable of
learning math or do you choose not to?

I choose not to accept nonsense conclusions justified by unsound axioms,
if that's what you mean...

Which axioms would those be?


Take the axiom of infinity, for instance. It declares an infinite "set", but it cannot do so with just the notion of set membership, so it inserts Peano's successor relation as well. There are no pure infinite sets. All infinite "sets" are sequences or other inductive structures, with order.

The axiom of choice is highly suspect, if not in what it actually states, then in its application. The axiom of induction is too limited by the faulty conclusions of limited induction.

You cannot divide a ball into five pieces and reassemble those pieces into two solid balls of the same size as the original, where measure is not ignored. I don't need to accept proper subsets being the same size as their proper supersets.
.

Relevant Pages

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