@amWhy No problem. I don't flag comments that are mathematically correct. Yours certainly is, but since I got a downvote from nowhere and the asker doesn't find my post useful, I see no reason to bother to fix it. I don't understand what's going on over there though; 2 people (not me) found it useless?
@user21820 I don't understand any of your or mine downvotes. I suspect it might be a case of "here's what I did: ................ . Tell me which is the correct answer." Despite none are correct. Perhaps a poor multiple choice question? I don't know.
@amWhy Well the asker doesn't have reputation to upvote/downvote, so all those must be coming from somewhere else.
@LeakyNun: In case you haven't read the second thread I linked to above, you may want to, since it is about some of these mathematical statements that are equivalent to some low-complexity arithmetical sentences.
@amWhy That's sad. I get that kind of downvotes on occasion too. Nowadays it's just single posts so I assume it's just something they don't like in that post.
It is an open problem to prove that $\pi$ and $e$ are algebraically independent over $\mathbb{Q}$.
What are some of the important results leading toward proving this?
What are the most promising theories and approaches for this problem?
Yup. I studied very hard after getting to know that I studied topology, real analysis, algebra but wasn't knowing this stuff like that conditional statement
As I had told you back then that I learnt Abstract algebra, analysis and topology without not being quite well with logic. I mean I saw patterns in the proof. How to derive contradiction, how to construct a proof... etc
I am not teaching logic like ZFC, axiomatic set theory stuff... Just basic predicates, quantifiers, informal and formal statements involving quantifiers, valid invalid argument forms, vacuous truths, methods of proofs
Basically discrete mathematics. No hodge podge stuff
these students are very much job oriented and only want methods to solve problems. I tried to lure them to pure maths by giving interpretations such as truth table of conditional statement, russell's paradox but I wasn't successful.
$\exists \epsilon$ such that $\forall \delta \gt 0$ there exists $x$ such that $0 \lt |x| \lt \delta$ but $|f(x)-L| \ge \epsilon$.
Reference book is Susanna Epp's discrete mathematics and it's applications
Wonderful book :)
Simple, lucid good for beginners...
I was thinking about using Kenneth Rosen but university had given preference to Susanna's. But these students don't look in that book. They want method to solve problems
No you don't need to explain that now! It was a bliss to understand truth table of conditional statement. I swear majority of my profs will not have any clue about it
Whatever I am teaching now I really wish my profs would have taught me. I cracked two national exams. Coming in top 75 in one and in top 89 in other
negating the statements, explaining the quantifiers, explaining $\epsilon-\delta$ definitions of continuity, these simple things were not covered in classes. I would go insane that my doubts weren't getting solved.