Re: infinity

On May 30, 8:21 am, David R Tribble <da...@xxxxxxxxxxx> wrote:
sophia wrote:
can any one give an example to which infinity can be compared ?

In set theory, the relative sizes of sets are compared by matching
up their elements one-to-one.

If all of the members in set A can be matched with a member in
set B, with no members in B left unmatched, then we say that
sets A and B are equipollent, or that they have the same cardinality,
or in simpler terms that they are the same size. But if there remain
unmatched members in B (regardless of which matching scheme
we use), then we say that set B is larger than A.

This kind of set comparison works on finite as well as infinite sets.

And yes, there are kinds of infinite sets that are larger than other
kinds of infinite sets. The simplest example is the set of natural
(counting) numbers and the set of real numbers.

Shouldn't you be able to "count" most (if not all) of the real
numbers?



See also:
http://en.wikipedia.org/wiki/Cardinality
http://en.wikipedia.org/wiki/Infinite_set
http://en.wikipedia.org/wiki/Infinity

.

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