**The Man Who Counted Beyond Infinity**

Georg Cantor was a mathematician who proved something quite amazing - there are numbers bigger than infinity!

He called these numbers "transfinite numbers" and he even developed an arithmetic for working with them. He denoted them by the Hebrew letter "aleph".

So what did Cantor do?

He formalized counting. He started with the integers {1,2,3,...} and asked what other sets could be placed in 1-to-1 correspondence with the integers. Instead of just saying there are an infinite amount of integers he denoted the number of integers by aleph0 and developed an arithmetic that in many ways treated aleph0 as a regular number. But he went further..

He showed that the rational numbers (fractions) could be placed in 1-to-1 correspondence with the integers. So counterintuitively, there are only as many rational numbers as there are integers. Not more!

But when it comes to irrational numbers, there are many more. He called this number aleph1 and he showed that it was different and bigger than aleph0. He proved that the number of subsets of the set of integers {1,2,3,...} is also aleph1 and he produced this amazing result..

aleph1=2^aleph0

He even asked if there was an aleph number between aleph0 and aleph1.

In his lifetime Cantor was ridiculed, not by the general public, but by his fellow mathematicians!

Cantor retired in 1913, living in poverty and suffering from malnourishment during World War I. The public celebration of his 70th birthday was canceled because of the war. He died on January 6, 1918 in the sanatorium where he had spent the final year of his life.

Today Cantor's work is part of every university math curriculum and is regarded as one of the most beautiful pieces of mathematics ever created. It stands apart from most advanced math because you don't need to know much math to understand it. In fact, all you need to know is how to count!

Content written and posted by Ken Abbott abbottsystems@gmail.com

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