Infinite Sums

We prove more results for Ordinal and Cardinal arithmetic. Including showing that we can apply division with remainders to ordinals. We use that to prove Cantor’s Normal Form Theorem. Finally, we give a proof of Konig’s Theorem for Cardinals.

In this entry we cover more basic results about ordinal arithmetic. We also prove the so-called “Fundamental Theorem of Cardinal Arithmetic”, and then we finish with a short discussion about cofinality of cardinals.

Here we show the classic result that the sum of 1/p, where p ranges over all prime numbers, is infinite.