Re: [jboske] RE: Anything but tautologies

[pycyn@aol.com]

In a message dated 2/14/2002 6:33:35 PM Central Standard Time, jjllambias@hotmail.com writes:

la pycyn cusku di'e

>A problem with {le du'u makau du li pa} is that 1, as a function, typically
>has no domain (well, its domain is the empty set) and its range is
>singleton
>1 (of course).

That's not correct. The domain of the function could be, for
example, the set of real numbers. It could be any set at all,
except maybe the empty set. That means that each real number
is mapped to the number 1 by that function. I'm not sure the
notion of function with an empty domain is at all meaningful.

Jeez, ya mean I've been teaching set theory wrong for 35 years -- including the adequacy proofs?  Of course 1 as a function has no domain: look at it, NO argument, ergo no domain.

<>So, the {makau} never gets relieved strictly speaking.  Or is
>always already relieved and so should not appear.

The {makau} gets relieved by the range values, in this case the
singleton 1.>

Sorry, I misread your formula, taking {makau} for the argument rather than the value. 

<Of course we need names for functions. What we don't need is
a place for the name in the predicate for 'function'!>

But the function of {fancu} is precisely to introduce/define functions -- not an easy thing to do otherwise -- at least wordy.