@user21820 ^

→ 1 message moved to trash

I refreshed the page I linked (which I've removed) just now, and see the comment is there. Apologies.

@user21820 can it be the case that it is undecidable (under ZFC) whether e+π is rational?

@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?

@LeakyNun I have no idea.

@user21820 hmm?

absolutely no idea?

I mean, e.g. if RH is false then it's provably false

(Riemann Hypothesis)

That is already non-trivial.

And I didn't try to check the proof.

I haven't heard about any similar result for rationality of e+π.

@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.

@user21820 I'll read it later thanks

@user21820 Well I received two down votes in succession (2 seconds apart, or most), followed by another downvote for my answer preceding the above.

@user21820 can it be checked whether e+π is equal to, say 1325465463456/1231353745253 in a finite amount of time?

@LeakyNun Hi! (I'm ducking out so as not to distract!) :)

@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.

@amWhy hi! any idea?

@LeakyNun Yes because we can prove it is not equal.

@user21820 why?

e,π are computable, so we can compute them to any arbitrary precision.

if it's equal, can you check it in a finite amount of time?

That's the side I don't know. Although I can be funny and say "yes" because it is not equal. =D

@user21820 :c

your program wouldn't halt if you write it as you described it

i.e. keep computing for more decimal places and check if they're equal

@LeakyNun You're using the wrong definition of computable.

@user21820 i mean if they were equal

Oh then yes that naive approach won't work, but there's no clear reason that we cannot prove it some other way.

@user21820 because the go-to way to disprove it is to compute it to a million decimal places

There may be some weird number-theoretic reason that e+π is rational.

One can't exactly rule such a possibility out so easily.

hmm?

no, it's an open problem

I know it's open. I'm saying you can't use naive approaches to think about it since there is no clear reason to do so.

See this:

Schanuel's conjecture implies that e,π are algebraically independent, and so e+π would be irrational.

@user21820 hmm

thanks

@user21820 wow that's nice

how do you test if a model is consistent?

@LeakyNun I don't really get this question. A model is not a formal system, so what would "consistent" mean?

Unless you're talking about science.

In which case we're not interested in consistency but rather explanatory and predictive power.

ugh, nvm then

@LeakyNun: Okay I'm going off for today. See you next time!

@user21820 see you

Hi @LeakyNun Remember you taught me basic logic?

@Mathmore ZFC right

Naah

Statements like $0=1 \implies 1=2$ is true

hmm

alright

I teach that stuff now

and then?

wait waaaat

how long ago was it when I taught you that

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

Thank you for opening my eyes.

I think that was July

On Mathematics general chat.

what

You taught me vacuous truth as well

how did you go from "learning a stuff" to "teaching a stuff" in two months

where are you teaching?

teaching Undergraduates

in Information technology department

what

of a local college.

how is that even

possible

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

what do you mean by you are teaching logic now?

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

hmm

that's nice

what are you teaching then?

like, an independent logic course?

Oh... as a course It's discrete mathematics

basic predicates, quantifiers, informal and formal statements involving quantifiers, valid invalid argument forms, vacuous truths, methods of proofs, elementary number theory, functions and relations

:o

how is it humanly possible

@Mathmore what is the negation of $\forall \varepsilon \exists \delta \forall x [0<|x|<\delta \implies |f(x)-L|<\varepsilon]$?

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 $|f(x)-L| \ge \epsilon$.

@Mathmore nice...

Halting problem was also there in syllabs

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

I'm still amazed how you went from not knowing it to teaching it in two months

@Mathmore

Were you mocking me? :D As I said I am NOT teaching ANY Hi-Fi stuff. Basic discrete maths only.

I am not mocking you :c

Well there were logic, discrete maths courses when I was Undergrad as well as grad but frankly they were ruined by profs

Instead I used to solve algebra, analysis, topology problems more efficienty.

I see

I don't remember being taught in classroom to negate the logical statement

let alone nobody explained me why false statement implies false statement is a true statement,

I see

I even started thinking that logic is not maths

well we usually use the analogy "the ground is wet" and "it is raining"

it is raining => the ground is wet

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

@Mathmore wtf

your profs? no idea about truth table?

They know the truth table. But they don't understand it.

Especially conditional statement $p \implies a$

$p \implies q$*

they know how to use it to show logical equivalence

I was frustrated as a student through my undergrad as grad as "quality" maths was absent

I'm sorry about that

Whatever I know (you can see my answers and questions on this site), is because I did self study

But that self study was directionless. Thank god I found MSE 2-3 years ago when I was doing MSc.

MSE is really great

I imagine it will help me a lot when I go through university

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.

@LeakyNun sorry for this pompous rant

no problem

come talk to us more in the general chat

not here?

@Mathmore anywhere

Okay