December 2011
Beginner
240 pages
6h 45m
English
Content preview from The Universal Computer
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Cantor: Detour through Infinity
some one particular set made up of some of those same elements, then
the diagonal method can be used to obtain a new set of those elements,
different from all the sets that have been labeled.
Let’s see how this would work if we begin with the set of natural num-
bers 1, 2, 3,.... We imagine putting some of these numbers into a package.
One package might consist of just the numbers {7, 11, 17}.Anothermight
consist of all of the even numbers. Now let us imagine using the natural
numbers themselves as labels, as in the following infinite array:
1234...
...
M
1
M
2
M
3
M
4
...
where each of M
1
,M
2
,M
3
,M
4
, ... is a package of natural ...
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