Georg Cantor (1845-1918), a German mathematician, first dared to think the counter-intuitive notion that not all infinite sets have the same size--and then he proved it: The set of all real numbers (including all of the decimal numbers representable on the number line) cannot be matched in a one-to-one pairing with the set of counting (or natural) numbers -- 1,2,3,4, . . . . Sets whose elements can be matched one-to-one with the counting numbers are termed "countable" -- and Cantor's result showed that the set of all real numbers is uncountable.
Cantor developed an extensive theory of transfinite numbers -- and poet (as well as philosopher and professor) Emily Grosholz reflects on these in a poem:
Showing posts with label countable. Show all posts
Showing posts with label countable. Show all posts
Friday, September 24, 2010
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