4
votes
4answers
258 views

How to Make an Introductory Class in Set Theory and Logic Exciting

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 ...
5
votes
7answers
323 views

Is there a name for this type of logical fallacy?

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 ...
4
votes
4answers
418 views

the role of logic in math and education

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 ...
9
votes
1answer
177 views

Difference between a Lemma and a Theorem [duplicate]

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 ...
8
votes
1answer
422 views

Is “A and B imply C” equivalent to “For all A such that B, C”?

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 ...
6
votes
5answers
460 views

trivial but non-trivial equivalence relations

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: ...
2
votes
2answers
393 views

Is most of the GM-AM Inequality in its codicil?

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 ...
2
votes
2answers
204 views

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).