Re: An uncountable countable set

Virgil wrote:
In article <45193afa@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <45189e62@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <45187864@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Han de Bruijn wrote:
Tony Orlow wrote:

Mike Kelly wrote:

Han de Bruijn wrote:

Mike Kelly wrote:

Han de Bruijn wrote:

Mike Kelly wrote:

What the hell are you talking about? Arguing with someone who can't
speak English is getting aggravating.
My English is much better than your Dutch.
So what? Your English is still too poor for this discussion to be
fruitful.
Still don't get the point, huh?

You are lacking even the most elementary form of politeness. It's very
impolite to cut of a discussion with somebody from a foureign country -
somebody who is doing his best to communicate with you - only because
you are obviously superior in expressing your thoughts within your own
mother's tongue.
You're a very rude person yourself, Han. I generally don't feel the
need to be civil to those who won't reciprocate.
I don't think I have ever found Han to be rude, except when he referred to my "babbling" recently. Ahem. But anyway, while we disagree on the actuality of any infinity, we have the open mind of spirited debate, and feel no need to get nasty.
I may be rude sometimes, but I never get _personal_ by calling somebody
an "idiot" or a "crank". Tony's "babbling" translates with Euroglot as
"babbelen" in Dutch, which is a word I can use here in the conversation
with my collegues without making them very angry (if I say "volgens mij
babbel je maar wat"). But, of course, I cannot judge the precise impact
of the word in English. Apologies if it is heavier than I thought.
Do you have the saying, "Shallow brooks babble, and still waters run deep"? I figured you picked up the usage from this forum, actually. It's meant, in English, to mean you aren't making any sense. :)

Furthermore, I have never had any trouble understanding what Han is saying, except where he is using some mathematical construct with which I am not familiar. His English is not bad, and blaming your disagreement on his inability to communicate is kind of low.
Thank you very much, Tony, for this sort of defense.
My pleasure. It seemed like a vacuous excuse. I get pretty sick of those diversionary tactics.

So, let's engage in lively debate, and maintain our civility, while chopping each other's arguments to pieces. Of course, this can only happen if we don't consider our arguments to be part of our anatomy. Otherwise, it gets personal.
You are misinterpreting virtually all my posts. You claim that you're
not dishonest so I have to conclude you're simply incapable of
comprehending written English. This makes this whole subthread
pointless.
I have only this kind of trouble with _you_ and nobody else on the web.
Really? You've never had anybody else other than me complain that you
misinterpret their posts? I suppose I must have hallucinated dozens of
posts I've seen of just that, then.

You've never had anyone other than me struggling to understand what the
devil you mean by your broken English? I must have hallucinated, for
example, "A little physics would be no idleness in mathematics", then
:)?
Well, that's a difficult type of quote. Han - I wouldn't mind working on exactly how you want to say that in English, if you like. :)
Uhm, since litteraly everybody is complaining ... Let it be an encrypted
message then :-)
Well, it seems to me that perhaps you're saying something like, "Those with their heads in the abstract should keep their feet in the concrete", though that sounds a little funny.

Math=Science?
Scientists, particularly those in the sciences most dependent on mathematics, tend to think that all mathematics is, or should be, a subservient to their particular fragment of science.

Mathematicians know better.
Define "better". Those that work in various areas of science share a notion which defines science. Theories which have no means of verification are not science, but philosophy. In mathematics, verification really consists of corroboration by other means, agreement between different approaches. In science, where you find a contradiction with your theory, it needs revision. So, the scientific approach to mathematics requires some criterion for universal consistency, as measured by the predictions of the various theories that comprise it. Where two theories collide, one or both is in error. I think that's better.
TO mistakes misapplication of mathematics, which is an error by scientists, as an error of the mathematics.

That's not what I said, and you know it.

When an application of mathematics to physics, or some other science, does not predict what actually is observed in that science, why does TO insist the problem is inherent in the mathematics alone and not in the improper application of mathematics to science?

It's not a matter of what's observed in physical science. I am saying that the general method of science can be applied to mathematics, where verification of a theory is through agreement with other theories as far as conclusions are concerned. Where two theories collide, and both seem sound, there is usually a generalization which includes both as parts, right? Like Euclidean geometry is now a category of geometry, eh? If the conclusions can't be reconciled into a single theory of some sort, maybe some of the assumptions have to be reconsidered.

The history of science is strewn with scientists getting their theories wrong and then having to change their minds about how things work.
The same holds true for mathematics. How long did it take to resolve the inconsistencies in set theory to the satisfaction of the mathematical community?
It hasn't been done yet to the satisfaction of all mathematicians, and probably never will be.

But mathematicians will all agree on the consequences of assuming a particular set of axioms even when they do not agree on which sets of axioms one should assume, for example the constructionists versus the formalists.


I agree with that also, although I think there is a little bit of disagreement over exactly how logical implication works when the premise is false.


What ever happened to infinitesimals?

Abraham Robinson.
The only major time that happened in mathematics was the discovery of non-Eucidean geometry, and Euclidean geometry was based mostly on the conlusins of science, not pure math.
If you say so. Somehow I thought theories about numbers starting at 1 and all being countable, or always positive, or always finite, or not having a square root if negative, were all theories that were overturned given later advances.

Originally, 1 was not considered a counting number, and even 2 was doubtful. But except for adding those and 0 to the naturals/ordinals, there has been no change in the counting numbers for a couple of millennia. That other things came to be called 'numbers' does not conflate them with the natural numbers, it is just that more and more things were discovered to have number-like properties.



Where calculus was invented, the theory took a long time to formally state. So, you're claim is simply wrong.

New discoveries, like calculus, do not invalidate prior work, they merely expand it. But things in the sciences like, for example, the phlogiston theory of combustion, were not just expanded but exploded.

Sure, in physical science, any consistent counterexample blows the theory, and people theorize all sorts of stuff about anything they want. In math, it's a whole other world, but it's related to science. They both have to be consistent. Math creates science, and science guides math. It's like yin yang, Man. :)
.

Relevant Pages

  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... My English is much better than your Dutch. ... example, "A little physics would be no idleness in mathematics", ... subservient to their particular fragment of science. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... My English is much better than your Dutch. ... example, "A little physics would be no idleness in mathematics", then ... subservient to their particular fragment of science. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... My English is much better than your Dutch. ... Scientists, particularly those in the sciences most dependent on mathematics, tend to think that all mathematics is, or should be, a subservient to their particular fragment of science. ...
    (sci.math)
  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... My English is much better than your Dutch. ... example, "A little physics would be no idleness in mathematics", then ... subservient to their particular fragment of science. ...
    (sci.math)
  • Re: Cantors Theory sucks
    ... > Tony Orlow wrote: ... > Mathematics is NOT the science of truth. ...
    (sci.math)