Christopher Menzel wrote:
>>> There are (as of course John and Pat know) 2^card(D) relations over
>>> any set (taking relations here to be sets of n-tuples).
>> Only if n=1.
>
> Only if D is finite. (01)
My point was that a relation over a single set is a set of 1-tuples;
but see it as yet another example of my terminological pickyiness. (02)
> The POINT, of course -- that D, no matter its
> size, cannot contain all of the relations over D -- holds regardless. (03)
Obviously. (04)
> I must admit that, like any good platonist, I was thinking of D as
> infinite, in which case what I say is true for all n. (05)
A relation over an infinite set is still an (infinite) set of 1-tuples.
(But see above.) (06)
> To cover the
> general case of D any size, insert "at least" above after "There are". (07)
At least, unless n=1. (08)
vQ (09)
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