Re: Cantor's definition of set

John Jones schrieb:
Stipulating that a set has no name can play fast and loose with what a
set is. I can name a set of cutlery. But if I use just the word set on
its own then I give the concept of a set.

If you want to denote the concept of a "set of cutlery" in
set theory. Then you cannot use the notion of a set directly.
Because you want to talk about an arbitrary set of cutlery
I assume.

Then you can use the powerset which exists in set theory
by means of the powerset axiom. And the union, which
also exists by means of the union axiom. This will allow
you to construct a set 5you probably mean by a "set of cutlery".

Lets see.

We have the set1 of cutlery: {fork1, knife1, ..}
belonging to family richards
We have the set2 of cutlery: {fork2, knife2, ..}
belonging to family adams
We have the set3 of cutlery: {fork3, knife3, ..}
laying around in the shop harrods
We have the set4 of cutlery: {fork4, knife4, ..}
laying around in the factory
We have the set5 which is the set2 after the
youngest of the adams family has stolen the knife
etc..

What do all these sets have in common, and can we
express this in set theory?

Surely.

S = "Concept of a set of cutlery" =
{ x |
x={y,z,..} & fork(y) & knife(z) & ... }

Or in shorthand:

S = Pow(Fork u Knife u ...)

More refinement is possible though. Like defining a
complete set of cutlery, where for each fork there is
one knife. And stipulating that a set of cutlery is
finite, etc..

But whats the big deal? Are you all insane?

Bye




.

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