Re: Calculus XOR Probability

In article <Iw777D.I6@xxxxxx>, *** T. Winter <***.Winter@xxxxxx> wrote:
In article <MPG.1e821881e8e37b9a98aaee@xxxxxxxxxxxxxxxxxxxxxxxxx> Tony Orlow <aeo6@xxxxxxxxxxx> writes:
Dave Rusin said:
...
"Forbidden"?

Mathematicians are a libertine, almost anarchistic group.

That's a laugh, coming from the guy who patiently tried to explain how I was
wrong about countably infinite sets, and then demanded that I either accept
that there are an infinite number of finite naturals or be banished to his
killfile, ala the Spanish Inquisition. Very open minded. If someone
responds to this post, maybe he'll see my response.

Is it? Using the standard definitions, axioms and whatever, it can be
proven that there are only a countably finite number of naturals.

Um, you mean "countably infinite". But I don't recall that in my
conversations with TO he claimed that there were uncountably many
naturals (except perhaps in a very circuitous way, e.g. by claiming
a falsehood, from which every other falsehood logically follows!)

No, the problem I had with Tony was just the opposite: he would claim
that there are only finitely many natural numbers (he referred to them
as "finite naturals"). I was under the impression he still believed that.

Tony's experience is, actually, precisely covered by what I wrote
about mathematical culture. As I explained to him there is absolutely
nothing wrong with considering other sets of "numbers" besides the
natural numbers. (Some of these sets may indeed by uncountably infinite.)
One may, for example, consider the set of all left-infinite
digit-strings ... a_4 a_3 a_2 a_1 where each a_i is in {0,1,...,9}.
It's a well-defined set, and on this set we can define addition and
multiplication in the grade-school way, and we can verify that the
associative, distributive, and commutative laws hold here, as well as
the existence of zero and additive inverses. (So it's a ring.)
But I also pointed out to him that it's not possible to linearly order
this set in a way consistent with sums and products. Well, that's not
a problem for me: I have no particular interest in this ring, so I
don't care that it can't be ordered. He is welcome to pursue it if it
interests him. That's what I meant by our "libertine" culture.

Unfortunately, Tony was not willing to abide by what I claimed to be
the one immutable law of society here: he was unwilling to state
clearly what it was that we studying and to live by the consequences
of that decision. (For example, the fact that there is no good
ordering in this ring did not prevent him from claiming that
"....3636363 is 1.25 times as large as ....272727 ".) Indeed, he
never really claimed to be studying this particular ring -- it was
just one candidate I proposed to him so I would know what the heck
we were talking about; he neither explicitly accepted this definition
nor ignored it.

Nothing is really forbidden -- you're welcome to pursue whatever
you like. The only requirement is that you define your terms and
clarify your assumptions, and then proceed logically.

I'm sure those of you following his postings have continued to see
this kind of nonsense -- an unyielding attachment to intuition even
when it is provably contradictory. As he suggests above, I have
stopped reading his posts. I had no idea that my personal refusal
to pay attention to someone meant that they were "forbidden" from
discussing the things they want. (Someone should tell the TV networks
that they are forbidden from broadcasting because I don't watch!)

Or perhaps I didn't make it clear enough: in an anarchistic society
no one can tell you to shut up; but no one can tell me to listen to
you either.

I do like the bit about the Spanish Inquisition, though. I had no
idea I had so much power. The rest of you had better watch it!
Remember -- NO ONE EXPECTS THE SPANISH INQUISITION !!1!

dave
.

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