On Wed, Oct 17, 2012 at 1:34 PM, Paul Tanner <upprho@gmail.com> wrote:
You started generalizing beyond coffee with your "Functional or "to
one" relationships are pretty well understood today, no need to imbue
them with mystical powers of action, or connotations of "belonging to"
or "contained within"" and such, and so the general definitions of
functions are now in play.

You should think of objects as members of a set, or likewise members in memory.  Each member has its attributes.

For example, if you're "2", a member of the set Z (integers) then your blueprint / template includes circuitry / a recipe for "adding".

You, "2" and another member of your set, say "5", both have the add method such that:

2.add(5) and/or 5.add(2) make plenty of sense.  The Z type of object knows "adding", i.e. the behavior "to add" belongs to the integer type.

In reality, I'm writing in a generic dot notation that doesn't exist.  2 .__add__(5) is how you'd write in in Python, but really 2 + 5, with + triggering __add__, is the expected syntax.
 

And this includes not in terms just of what sets are and are not in
play but of how formulas are related to the use of the term
"function". Some uses of the term refer to the formulas that determine
the set of outputs, and even refer to the output itself as in "y is a
function of x" and so on.

Sets tend to be over-valued thanks to Russell-Whitehead.  They allow only unique items, no duplicates.  That's a restriction we don't always need.

In any case, I recognize sets as a good place to start using dot notation, with S.intersection(T) or S & T representing members in common, another set.

S.union(T) would be their combined elements with no duplicates.  So again, an object with a behavior (union, intersection) and taking an argument (another set).

Python 3.2.3 (v3.2.3:3d0686d90f55, Apr 10 2012, 11:09:56)
[GCC 4.0.1 (Apple Inc. build 5493)] on darwin
Type "copyright", "credits" or "license()" for more information.
>>> setA = {"A", "B", "C"}
>>> setB = {"B", "C", "R", "Q"}
>>> setA.union(setB)
{'A', 'Q', 'C', 'B', 'R'}
>>> setA.intersection(setB)
{'C', 'B'}

More than your TI calculator will do, and for free.  Free download. 

Raspberry Pi is for like $35 and will do this, but you still need keyboard and monitor.

Parents?  Any input?  You live in a democracy remember? (ironic joke).

Kirby