Beyond Infinity, Summer 2020


Teacher: Jade Nine

Room:
Time: Sunday 1:15PM - 2:45PM
Grades: 9-12


Description: Join this course if you want to dive into the deep end of mathematical logic. We will discuss how to build numbers as sets, and then use this to systematically build up different kinds of infinite numbers - some of them larger, possibly much larger, than others. We will also find some logical concepts and proof techniques that are rarely (if ever) found in arithmetic, algebra, or even many other areas of math and science, yet are natural in their own way; such concepts include consistency and independence, and famous results such as Gödel's Incompleteness Theorems and Cohen Forcing. Prerequisites: students should be comfortable with logical notation (including symbols for logical and, logical or, and implication); students should also have experience working with axioms, and understand the distinction between axioms and theorems. On the first day of class, we will define "partially ordered set" and "well-ordered set," you can look these up in advance if you want.


Homeworks

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