Dangerous Knowledge : Georg Cantor
June 30, 2008 6 Comments
Inspiration for following few Dangerous knowledge posts is BBC doucumentry known as “DANGEROUS KNOWLEDGE” which is a must see and recommended.
“Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845 – January 6, 1918 ) was a German mathematician. He is best known as the creator of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are “more numerous” than the natural numbers. In fact, Cantor’s theorem implies the existence of an “infinity of infinities”. He defined the cardinal and ordinal numbers, and their arithmetic. Cantor’s work is of great philosophical interest, a fact of which he was well aware.The harsh criticism has been matched by international accolades. In 1904, the Royal Society awarded Cantor its Sylvester Medal, the highest honor it can confer.”
“Cantor was the first to formulate what later came to be known as the continuum hypothesis or CH: there exists no set whose power is greater than that of the naturals and less than that of the reals (or equivalently, the cardinality of the reals is exactly aleph-one, rather than just at least aleph-one). Cantor believed the continuum hypothesis to be true and tried for many years to prove it, in vain. His inability to prove the continuum hypothesis caused him considerable anxiety.”
“The difficulty Cantor had in proving the continuum hypothesis has been underscored by later developments in the field of mathematics: a 1940 result by Gödel and a 1963 one by Paul Cohen together imply that the continuum hypothesis can neither be proved nor disproved.”
Full Article at : http://en.wikipedia.org/wiki/Georg_Cantor
