Cantor and Infinity

After a brief respite for evaluation, I posted a new essay with more details on Georg Cantor’s definition of Infinity. You can read it here at www.jacob2012.com/essays/cantor. This essay discusses the impact of Cantor’s work in mathematics and infinity, specifically the differences between finite numbers, a countable infinity, and uncountable infinity.

We seldom, if ever, come upon an uncountably infinity in our daily lives. We may think that Bill Gates and Warren Buffet have an infinite amount of money – and $56 billion may seem like an infinite amount of money that would take an entire lifetime to spend, but it is still finite. An example of a countable infinity are the natural or counting numbers (0, 1, 2, 3, 4, 5, …….). Even the set of all fractions – the Rational numbers – are a countable infinity since they can be mapped directly onto the natural numbers.

An example of an uncountable infinity are the Real Numbers. You can think of the Reals as all of the numbers between 0 and 1 – also denoted as the closed set [0,1]. If every person on Earth spent their entire lifetime counting the Real Numbers, we would never, ever count them all!

For a more in-depth discussion, go here http://pirate.shu.edu/projects/reals/infinity/uncntble.html and infinity http://www.mattababy.org/~belmonte/Publications/Books/CSaW/5_infinity.html

If you really concentrate on infinity and you get a headache or stomach-ache, then you’re on the right track in your attempt to feel and/or intuit infinity. Keep up the good work!