Re: Dik T. Winter says: Definition: sum{i in N} i = 0

On 21 Jun., 16:16, Klaus Cammin <netzkl...@xxxxxxxx> wrote:
Did Michalangelo's David exist before Michelangelo exhumed it from the
marble block? Did Schiller's Glocke exist before he wrote it? No.

Yes, that did exist.

This is a strange but nevertheless possible claim.


Don't you know that sculpturists actually work that
way? They say as a helpful working hypothesis: "The thing I want to do is
already there, I just have to beat off the superfluous rock."

It existed in their *minds*. Even the most hardbitten materialist must
admit that having something in mind is an objective fact. And this doesn't
have to be platonic at all.

If David actually was in the block or not, is irrelevant. There was a shift
of perspective here, utterly important and helpful for Michaelangelo to
create his David.

An important math example for shift of perspective is completeness of
reals. After these many postings I'm convinced, that the notion of "a
sequence approaching its limit without ever reaching it" actively prevents
understanding this.

Nevertheless every irrational number is nothing but such a sequence.

You have to put that aside and focus your mind on the least upper bound.
Doing that enables you to see, that every bounded subset of reals splits
all reals such that all elements of that subset are on the left of the LUB,
and on the right there are none. Which side the LUB is, is another
question. Mayhap both alternatives are valid.

As there is a artional between every pair of LUBs there cannot be more
LUBs than rationals.

Nobody could "apply" these items in any way.

The application is innermathematical in the first place. If and where an
outbound application takes place, remains unclear, but no damage.

So yes, in a way the axioms say, what state you have to put your mind in to
create good math. You're free to follow it or not, but to say the least,
good math resulting might be a questionable circumstance.

The innner structure of math might be viewed as sensible working hypothesis
for the actual outbound application. And the notion is, that the better,
i.e. the more consistent it is, the better the application.

So your argument, that nothing would change practically if the axiom of
infinity would be abolished, actually works against you: it's just another
good reason to stick to it. It's fitting all nicely, why return to crap
again?

For the sake of truth. Accepting a God as the reason of thunder or
daylight also is fitting nicely all practical life.

Same is true with the
prime. It did not exist for any human being. (Perhaps it did exist or
had existed elsewhere.)

So nothing exists, if it does not exist for a human being or other living
creature?

No *ideas* exist, which are not in some mind. Brains exists even if
there is no spirit inside.

I don't care. If math is just about notions, which don't exist
any longer with the disappeareance of mankind, it's fine with me.
"Existence" is a context dependent term.

No, the axiom is obviously wrong.

Why? That infinitely many primes exist, was proven long before set theory
came up. Are you denying that these exist?

It was proven, by a proof by contradiction, that every given finite
set of primes is incomplete.

Infinity was always a matter in mathematical history. "Potential infinity"
has been proven insufficient and contradictory, hence it was abandoned.

Dann kam man vom Regen in die Traufe.

Your strange assertion, that some naturals exist and others don't, does not
make any sense. Demanding the capability of "application" is an insane
restriction.

Application is not the central issue. Distinguishing two numbers is
crucial to se that thy are different.

But I can prove my assertion that the drug of infinity is faulty.

Purely finite math is rotten, as Dik indicated, that infinite math even
produces results for finite numbers. However it would be nice, if you
explained to me in simple words, how you want to accomplish that.

I cannot prove my existence - but not to a solipsist.

Regards, WM

.

Relevant Pages

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