In order to prove that F is a

countably strict-set contraction, we first consider

p] have lateral limits everywhere, and at most

countably many discontinuities.

A subset of X is I-sequentially compact if and only if it is I-sequentially

countably compact.

Comparing the Book of Sand with the two models discussed above, we have the following situation: a

countably infinite book with a leaf at each rational number strictly between o and 1 will satisfy (b) but not (a), while the hyperfinite book with N leaves of thickness 1/N will satisfy (a) but not (b).

1] can be expressed as a disjoint union of a class C of

countably infinite sets, the cardinality of C being [[omega].

k] is of measure zero if and only if for every [epsilon] > 0 there exist

countably many closed k-dimensional rectangles [R.

Let [mu] be a

countably additive, regular, vector valued, Borel measure on R taking values in [B *.

When considering the transition from finite to infinite iteration in the

countably infinite case, the BMI and APOS Theory appear similar.

We will show that the solutions are generalized functions (rather than ordinary function), which reflect the above fact that the corresponding "measure" are finitely additive signed measure (rather than

countably additive measure) of unbounded variation.

Since they correspond to statements, it follows that truths cannot be more than

countably infinite.

The key notation describing limited price adjustment will be a vector [PHI] (possibly with a

countably infinite number of elements); the sth element of [PHI], called [[phi].

That is, a part (a 'half') of the entire collection of positive whole numbers is as numerically large (as

countably large) as the entire set itself