May 2014
Intermediate to advanced
350 pages
9h 55m
English
Content preview from Computing
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120 ◾ Computing
Nto N, or equivalently, the number of problems, is the same as the
number of subsets of N, which is the powerset of N. Its cardinality
was shown to be
ℵ
1
. However, the number of possible programs
that have been, or can ever be, written cannot exceed
ℵ
0
. So,
using a straightforward cardinality argument, we have shown
that there must exist problems/functions for which a computer
program cannot be written.
Many practical problems in computer science, ranging from the
determination of running time of an algorithm to proving the opti-
mality or even the correctness of an algorithm, are oen resolved using
cardinality-based a
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