Set Theory in the Flesh :: Numbers Mathematics Essays

Set Theory in the Flesh The idea of infinity has been around for thousands of years. It it impossible to even conceive of this number or anything that pertains to the infinite. There is always one more. A billion is a fairly large number, 1 with 9 zeros after it. If one counted by seconds without breaks, it would take over 32 years to reach it. A Google, is a number written as 1 with one hundred zeros after it. One couldn't even count the number of lifetimes it would take to count to this number. Yet there are even much higher numbers such as a Googleplex. This number is one with a Google zeros. It would take far far too long to even write out the number. If the entire known universe was packed with quarks, the smallest known material, the number of quarks would not add up to a Googleplex. Compared to infinity, though, this number is as far away as the number one. Set theory is an area of mathematics that deals with inconceivable numbers, and bottomless concepts such as infinity. As it turns out there are many different kinds and orders of Hartmann 2 infinity that were documented by George Cantor, who opened up this area of math for the world. One way of describing these different levels of infinity is with Cantor's theoretical "Hotel Infinity" which is also an Allegory of his work and struggles in set theory. The story is interesting and also explains the fundamentals of infinity. Cantor and his assistant built a wondrous hotel that was made in such a way that there are infinitely many rooms. When he makes this hotel, his enemy Mr. Kronecker, criticizes itsaying that it's impossible and breaks the material of logic and should therefore be destroyed. Kronecker was a real person who criticized Cantor's works from the start trying to get it dismissed as not real mathematics. However, Cantor was able to publish his works, and in the story, his famous hotel was able to be printed in news paper advertisements. When the hotel finally filled up with an infinite number of people, Cantor's assistant didn't know what to do. Finally, Cantor told him to make everyone move from their room to a room that is numbered one higher than the previous one they were in. By doing this, Cantor was able to make room for one more person.