Re: Cantor's definition of set

John Jones <jonescardiff@xxxxxxx> writes:

On Nov 1, 9:56?pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
John Jones <jonescard...@xxxxxxx> writes:
On Oct 31, 10:05?pm, Marshall <marshall.spi...@xxxxxxxxx> wrote:
On Oct 31, 2:13 pm, John Jones <jonescard...@xxxxxxx> wrote:

I have flown high, I have squeezed between Atlas' shoulders and the
earth that rests upon them, I have plumbed the watery depths and
lifted the pebbles at the bottom of the abyss, and I can say to you
that mathematics has not given us an axiom of order, nor shall it
ever. My beard is long and whispish, I am the seeker of seekers, away
with idle pursuits.

I have to give you credit: you write better than any other troll
I've come across. I really wanted to make fun of the above,
but in the end I couldn't because I have to respect good writing.

However good writing does not necessarily mean good mathematics.

Since you say there's no axiom of order (or whatever of order)
in mathematics, I wonder what your response is to writings in
order theory.

http://en.wikipedia.org/wiki/Order_theory

Are they not part of mathematics? Inconsistent? E-vil?
Or what would you think of a mathematical *definition*
of order. Like, say, a binary relation that is antisymmetric,
transitive, and total.

Marshall

PS. "Wispish" was a very interesting choice, in contrast
to the more obvious "wispy."

Order might be defined in mathematics: by repeated application of a
function where each application yields a figure in an ascending
series. We might then say that this ascending series is an example of
order.

you see, you can vaguely make out something there.

But then I must stipulate size as representative of order.
There is no reason why I should do this, and disallow other parameters
as indicative of order.

right -- is anything looming through the mist yet?

A 'sequence' of numbers, such as the real numbers is not a
mathmatically generated order but is a reading order.

no, the smirr grows heavy again

We must excise the notion of order from sequence.

you mean there *is* a notion of sequence?

now try again ...

- Show quoted text -

Yes. There is a notion of sequence.

Are you feeling alright?

fine, thanks.

now, try again,
otherwise we'll think that you're after the would-be "smart" one-liner,
rather than philosophy.

goodness knows where we could have got that idea from ...

(hint: if there is no notion of order, there can be no notion of sequence)

--
Alan Smaill
.

Relevant Pages

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