All Questions
8 questions
53
votes
7
answers
8k
views
Zorn's lemma: old friend or historical relic?
It is often said that instead of proving a great theorem a mathematician's fondest dream is to prove a great lemma. Something like Kőnig's tree lemma, or Yoneda's lemma, or really anything from this ...
- 18.7k
34
votes
23
answers
29k
views
Textbook recommendations for undergraduate proof-writing class
I am teaching the proof-writing class (for the 3rd time) in the Fall and plan to buck the party line and use a different text than the default Bond and Keane. My parameters are as follows:
Logic, ...
19
votes
14
answers
4k
views
Excellent uses of induction and recursion
Can you make an example of a great proof by induction or construction by recursion?
Given that you already have your own idea of what "great" means, here it can also be taken to mean that the chosen ...
17
votes
4
answers
3k
views
Languages beyond enumerable
A language is a set of finite-length strings from some finite alphabet $\Sigma$.
It is no loss of generality (for my purposes) to take $\Sigma=\{0,1\}$; so a language is a set of bit-strings.
...
- 151k
5
votes
2
answers
2k
views
Any suggestions for a course in Mathematical Logic?
I am teaching a topics course for Mathematics majors (at Temple), and am considering Logic as the topic. I was wondering if people (a) have suggestions for an appropriate text and (b) how much might ...
4
votes
3
answers
507
views
Defining negation
I'm currently coauthoring a book intended to teach first-year students basic proof techniques. One of the chapters, written by my coauthor, is about basic logic. In that chapter the negation of a ...
- 18.7k
1
vote
0
answers
106
views
The proposition associated with a set
Given a set $U$ and a set $A \subseteq U$, is there an accepted symbol for the proposition $p$ over the universe $U$ such that for each $x \in U$, $p(x)$ is the assertion that $x \in A$? (The symbol $...
- 19.7k
0
votes
1
answer
2k
views
Dual of Zorn's Lemma? [closed]
It seems to me that the dual of Zorn's Lemma should be true: if $S$ is a non-empty partially ordered set and every chain of $S$ has a lower bound in $S$, then $S$ has at least one minimal element.
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