My infinity’s bigger than yours
An article from Scientific American explains how Infinity Comes in Different Sizes.
According to the article, the 19th century German mathematician Georg Cantor showed …
… there are more real numbers packed in between zero and one than there are numbers in the entire range of naturals.
I remember being blown away by the concepts of “countably infinite” (for example, the whole numbers 0, 1, 2, 3, … is a countably infinite set) and “uncountably infinite” (for example, the number of all numbers – that’s all the rationals, irrationals, complex numbers, etc.)
Cantor created Set Theory, a topic that was used and abused in secondary schools for many years. According to this Wikipedia article, after developing the concept of transfinite numbers, Cantor took himself a little too seriously and died a seriously depressed man.
I can’t resist concluding with Einstein’s profound quote:
Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.
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19 Aug 2007 at 7:17 am [Comment permalink]
But, sure about human stupidity! ^.^
12 Nov 2008 at 6:44 pm [Comment permalink]
Human thought is an infinite set of infinities, because it can encompass the whole universe and every thing inside it. Once you have imbibed this concept, you also become infinite.
7 Feb 2010 at 6:34 pm [Comment permalink]
[...] l’originale (in un articolo molto interessante per altri motivi) lo potete trovare quì. [...]