Re: Request for Review/Tutorage of Amateur Proofs

Am Thu, 27 Mar 2008 13:11:59 -0700 (PDT) schrieb MoeBlee:


And, Moe, we DO use (at least) two different [symbols] for the empty set
- as you know. If we refer at it as set we usually write "(/)"
(the empty set symbol). And if we refer to it as natural number zero,
we usually write "0". (No?)

Not me.

Ok.

Not a lot of authors.

Huh? Of course a lot of authors do! Halmos, Enderton, Ebbinghaus,
... (Actually, I would dare to claim that MOST modern authors do
exactly that.)

I see what I wrote was ambiguous. I didn't mean that there are not a
lot of authors who do; rather I meant that no matter what those
authors authors do, there are a lot of other authors who do otherwise.

Really? Modern authors?!


I.e., "Not a lot of authors" was meant as "There are a lot of authors
who don't bother to use different symbols or use them interchangeably",
which does not dispute that there are a lot who do use them always
distinctly.

Well, Wikipedia does not even _mention_ the possibility to denote
the empty set (_as such_) with "0":

"The empty set is denoted by either one of the symbols
"\varnothing" or "\emptyset", derived from the letter Ø in the
Danish and Norwegian alphabet, introduced by the Bourbaki group
(specifically André Weil) in 1939."

Source:
http://en.wikipedia.org/wiki/Empty_set

The german entry adds the following sentence (ad hoc translation):

"In some older books 0 (zero) is used."

Right. For example in Halmos' "Measure Theory"; but in his "Naive
Set theory" he already uses "(/)" (the empty set symbol).

Actually, I'm used to see the _definition_

0 := {}
or
0 := (/)

in modern textbooks concerning (axiomatic) set theory.


F.
.

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