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


Tony Orlow wrote:
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.

Please state the axiom of infinity.

There are no pure infinite
sets. All infinite "sets" are sequences or other inductive structures,
with order.

I have no idea what your definition of "a pure set" is. Pray provide a
definition.

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,

Not in real life, no. It's hard to cut non-measurable slices of a ball
by hand.

where measure is not ignored.

Private use of the word measure again, I guess.

I don't need to accept proper subsets being the same size as their proper supersets.

Set theory doesn't say proper supersets are the same size as their
proper supersets. Set theory doesn't talk about "size" as far as I
know.

Set theory says there are sets that can be bijected with some of their
subsets. Do you accept that?

--
mike.

.

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