*5.15:*

templates for subtype association:

**adda/oop/type cluster/**templates for subtype association:

[6.1: mis:

"( . having types specifying which subset relations exist)??

doesn't neatly show the relation of irrationals

irrationals are simply the reason

why some reals are not Q's !

. what is the purpose of knowing how they are related?

isn't it just to know type compatibility?

if you produce an irrational,

you call it a real,

and if you didn't want symbolics

then you'd call it a float .]

. the mgt for type clusters(eg numbers),

may have some reusable code in that there are

many type clusters in which the subtypes have

values that are subsets of each other; eg,

N subsets Z subsets Q subsets R subsets C .

. number is also an example of there being

*another way of describing subsets:*

**superset decomposition**

(showing how a set is composed of other sets).

. saying which subset relations exist

doesn't neatly show the relation of irrationals

(ones not expressible as a ratio, and

having an infinite and non-recurring expansion

when expressed as a decimal).

N = 0.. infinity;

Z= {+1,-1}*N;

Q = {Z/N, Z};

irrationals = {pi, e, 2**(1/2), ...}:

pi/4 = +(^i=0...infinity| (-1)**i /(2i+1) )

pi/2 = *(^i=1...infinity| (2i)**2 /(2i)**2-1) )

pi = 4 / (1+ 1**2 /( 3+ 2**2 /(5+ 3**2 /(...)))

e = (1+1/infinity)**infinity .

R = {Q, irrationals, repeaters}

C = {i*R + R, R} -- i = (-1)**(1/2)