I am teaching a "proof techniques" class for sophomore math majors. We start out defining sets and what you can do with them (intersection, union, cartesian product, etc.). We then move on to ...
Consider a statement of the form: $A$ implies $B$, where $A$ and $B$ are true, but $B$ is not implied by $A$. Example: As $3$ is odd, $3$ is prime. In this case, it is true that $3$ is odd, and ...
My question is somewhat related to this discussion: Is Mathematics one big tautology? I have a computer science background and I have always approached math from the logic point of view ...
What essentially is the difference between a lemma and a theorem in mathematics? More specifically, suppose you come across a general result while solving a mathematical problem, what are the ...
So I mostly study PDE, harmonic analysis, image processing, and so on, but for whatever reason I decided to be a TA for an undergraduate "introduction to proofs" course this semester. I suppose I ...
Define a binary relation $R$ on a set $A$ by saying $xRy$ iff $x$ and $y$ have the same whatever. "Whatever" is of course some specified function on $A$. This is a "trivial" equivalence relation: ...
Let’s define the codicil of the Geometric Mean – Arithmetic Mean Inequality to be the statement that if the means are equal, then all the terms are equal. Then: I conjecture that most of the GM-AM ...
What are good elementary examples for teaching/introducing/learning about Intuitionistic Logic or Heyting Algebras?
For example, I have heard of a topological one wherein negation means the interior of the complement (but still would like a reference).