Re: set of 8 positive integers, the sum of any 5 of which is prime

In article <1132428778.573631.150010@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Trav <lzwnews@xxxxxxxxx> wrote:
>Pubkeybreaker wrote:
>> We had this very debate in Math 55 many years ago.
>> It was a somewhat long and heated debate.....

>> Andrew Gleason was leading the class. Perhaps you would like to
>> debate this with him? I will use the same example he gave:

>> You have a set of 500 pieces of paper. You would like to argue
>> that the set has size = 1 because the pieces are indistinguishable?
>> Ridiculous...

>> Or take another set of pieces of paper; this time with (say) 300
>> sheets.
>> Call them sets A and B. They are both finite. I take a piece from
>> set A
>> and a piece from set B. I put them together and then place them aside.
>> I continue until set A is exhausted. Look Ma! There are still sheets
>> left in set B. We can't put them into 1-1 correspondence! They must
>> be different sizes! Yet you would argue that they are both the same
>> size (1).

Indistinguishable does not mean identical. If we have 8
indistinguishable balls in an urn, we can draw them out
one at a time until the urn is exhausted, and place them
in 8 distinguishable positions. At that time, we can
refer to any specific one by its position.

>> I will take Andrew Gleason's teaching over what is written in
>> Wikipedia.

>Wow, amazing. You're rejecting not just what's said in wikipedia, but
>everywhere, in every book on elementary set theory (or even first-order
>logic) I've read about. I've heard of people rejecting the Continuum
>Hypothesis or even the Axiom of Choice, but this is the first time I've
>heard of someone rejecting the Axiom of Extensionality.

>I give up. It is beyond me.



--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
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