Re: Questioning the defintions of set and element.


"David C. Ullrich" <dullrich@xxxxxxxxxxx> wrote in message
news:583m14h0nt5joo639vtn0d4tcoa45q97ff@xxxxxxxxxx
On Thu, 1 May 2008 16:50:16 +0100, "Mark" <user@xxxxxxxx> wrote:


"David C. Ullrich" <dullrich@xxxxxxxxxxx> wrote in message
news:e1oj14p69s4p4a15r46t4qtgkhnis70ms5@xxxxxxxxxx
On Thu, 1 May 2008 14:09:47 +0100, "Mark" <user@xxxxxxxx> wrote:


"David C. Ullrich" <dullrich@xxxxxxxxxxx> wrote in message
news:k0fj14lbq30cmomiiaoc1f513b35bu53jr@xxxxxxxxxx
On Thu, 1 May 2008 12:55:46 +0100, "Mark" <user@xxxxxxxx> wrote:

Hi, most definitions of element and set I have come across, say
something
like,

An element is any object of our perception or of our thought.

You found this definition where, exactly?

In formal set theory the notions of "is a set"
and "is an element of" are _undefined_.

[...]

From, "Discovering Modern Set Theory by Winfried Just, Martin Weese,
American Mathematical Society"
http://books.google.co.uk/books?id=x74azoKzb_MC&pg=PA1&lpg=PA1&dq=%22our+perception+or+of+our+thought%22&source=web&ots=EEHVpDqYX5&sig=Tg7he0U1spehvNQf89utd6oefhA&hl=en

"By a "set" we mean any collection M into a whole of definite, distinct
objects m (which are called the "elements" of M) of our perception or of
our
thought." - Cantor

It's a good thing that you included the fact that they cite Cantor for
this.

Do the authors say that this _is_ the definition of "set", or do they
just say that this is what Cantor's definition _was_? (That was
a long time ago...)



David C. Ullrich

No, they don't, but are there any newer definitions?
I havn't seen any.

Are you deaf or what? There is _no_ definition of "set"
in standard mathematics. That's a fact, and it's not going
to change just because you refuse to accept it.

Are you blind or what?


You have various options here. Three among many
others:

(i) Remain convinced that there _is_ such a definition
and for some reason everyone here is lying.

(ii) Remain convinced that there _should_ be such a
definition and the fact that there isn't means that modern
mathematics has it all wrong somehow.

(iii) Believe that there is no such definition and try to
understand why not; try to understand how we can
get along without such a definition; try to understand
how in fact there _must_ be _something_ in mathematics
that has _no_ definition whatever.

I'm not sure whether you're adopting (i) or (ii). If
it's (i) it's hard to understand why you continue
talking to all of us about this - maybe you're hoping
someone will slip at some point and finally tell
you what the definition is? (No, that's not going to
happen - we're all much too good at maintaining
elaboarate conspiracies).

If it's (ii), well, typically when an amateur is convinced
that the entire mathematical community has something
wrong it turns out, surprise, that the amateur is wrong
about something.

If, as it seems, you actually want to understand the
non-definition of "set", you need to take attitude (iii).
This requires that you first stop asking what the
definition is - that question has been answered. And
then _after_ that, if you want to understand the various
issues mentioned in (iii) above, all you need to do is
go back and read this thread more carefully, without
your erroneous preconceptions.
David C. Ullrich

My question was answered a good few posts ago, why are continuing with this.
All I was asking was if elements need to share some common property in order
to be grouped into a set.
Whether or not a set is defined in modern set theory is irrelevant. Get over
it.


.

Relevant Pages

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