Kardinalna aritmetika

The homework is optional, but worth 10% of the course mark if you choose to complete it. You can complete it as an individual or as a pair.

Illustrate some aspect of the ordinals or the aleph cardinals either by writing a 2-page essay (in English or Slovene) or by drawing a suitable picture. 

Your essay or picture should ideally be expository in nature, aimed at explaining or illuminating your chosen topic to a mathematically literate person who does not know the area (for example, to a high school student that is interested in mathematics).

Some possible more specific themes are:

• Counting through the smaller ordinals using appropriate notations (e.g., arithmetic notation).
• The peculiarities (or beauties) of ordinal (or aleph cardinal) arithmetic.
• Ordinal notation systems and/or normal forms. for example Cantor normal form.
• Goodstein's theorem and its proof using transfinite induction up to \epsilon_0
• Initial ordinals as cardinal representatives amongst the ordinals.
• Other themes of your own choice (you are welcome to consult with me).

Please submit your work in pdf format by email to Alex.Simpson@fmf.uni-lj.si by the deadline of 15.00 on Friday 6th May 2022.