A k-cell R is a subset of Rk of the form R= [a, b] x [a2, b] x [ak, bk], with 2.4 Definition For any positive integer n, let J, be the set whose elements are the integers 1, 2, ..., n; let J be the set consisting of all positive integers. For any set A, we say: (a) A is finite if A~J, for some n (the empty set is also considered to be finite). (b) (c) A is countable if A~ J. (d) A is uncountable if A is neither finite nor countable. (e) A is at most countable if A is finite or countable. A is infinite if A is not finite. Countable sets are sometimes called enumerable, or denumerable. For two finite sets A and B, we evidently have A B if and only if A and B contain the same number of elements. For infinite sets, however, the idea of "having the same number of elements" becomes quite vague, whereas the notion of 1-1 correspondence retains its clarity.