Mathematics of Infinity Course at The Beekman School
This course will take us through the changing Mathematical conceptions of Infinity down through the centuries, with particular emphasis given to the life and work of Georg Cantor in the late 1800's.
- Zeno's Paradoxes in General
- Achilles and the Tortoise
- Crossing the Room
- Pythagoras: His Philosophy and Work
- The Pythagorean Theorem
- The Emergence of Irrationals
- Georg Cantor: His Life and Work
- Sets and Subsets
- Counting Subsets
- Equivalent Sets
- Cardinal Numbers
- Infinite Sets
- Countable Sets
- The “Hilbert Hotel”
- Uncountable Sets
- Transfinite Numbers
- Russell's Paradox and other Paradoxes
- The Power Set Theorem
- The Continuum Hypothesis