This week, we continued discussing infinite sets of numbers, bijections, and modular arithmetic (alongside Pythagorean triples).
Here are some challenge problems to consider!
Are there natural numbers such that ? If so, find them, if not, explain why. Are there such that and exactly two of a,b,c are divisible by n? If so, find an [...]
For the first week, we explore basics of functions and permutations, picking up basic notation that we will use throughout the course.
On Tuesday, we obtained a definition of a function after first learning an informal definition of 'set' and examining a number of examples of functions. Along the way, we picked up some basic [...]