Franklin Pezzuti Dyer

general recent conversations

$Mathematics$ Discussion on answer by jjagmath: Fin…

Imported from a comment discussion on math.stackexchange.com/q...

Dec 1, 2023 16:26

No need to go on the offensive. :/ I have no issue with a recursive definition (although, now that you mention it, and as @Angelo suggests, you could definitely be more explicit about this). My objection is that the OP is looking for all continuous solutions. So if you're giving all solutions (including non-continuous ones), then you have not answered the OP's question.

Franklin Pezzuti Dyer

Dec 1, 2023 16:26

I think you need the additional condition that g(4)=g(2)+1, else we might not have continuity at the places where you are gluing together the pieces of the piecewise definition. Otherwise, good answer!

$Mathematics$ Discussion between Franklin Pezzuti D…

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Franklin Pezzuti Dyer

Jul 10, 2023 17:22

Understood hehe

Franklin Pezzuti Dyer

Jul 10, 2023 17:20

"Chang and Kiesler" is one book, "Model Theory 3rd ed". I really like that one myself, it's really dense though

Franklin Pezzuti Dyer

Jul 10, 2023 17:20

Neato. Just for fun?

Franklin Pezzuti Dyer

Jul 10, 2023 17:17

just out of curiosity ;)

Franklin Pezzuti Dyer

Jul 10, 2023 17:17

@lafinur You wouldn't be working through a model theory book, would you? Maybe Chang and Kiesler?

Franklin Pezzuti Dyer

Jul 10, 2023 17:16

@lafinur Sure thing, glad it helped! :-)

Franklin Pezzuti Dyer

Jul 10, 2023 17:16

For instance, consider $\Gamma = \{x\land y, \neg(x\lor y)\}$. By your reasoning, one might say "define $f$ such that $f(x\land y) = 1$ and $f(\neg(x\lor y)) = 1$, then $f(\gamma) = 1$ for all $\gamma\in\Gamma$ and therefore $\Gamma$ is consistent". But this $\Gamma$ certainly is not consistent. Really you should be assigning values for $f(x)$ and $f(y)$, and the truth value of each formula involving $x,y$ is determined by these truth assignments. You'll find that no assignment of $x,y$ makes both formulas of $\Gamma$ true.

Franklin Pezzuti Dyer

Jul 10, 2023 17:16

@lafinur Regarding your argument, it looks like you're misunderstanding what a valuation does. It doesn't assign a true/false value to every formula, but rather a true/false value to every sentence symbol (assuming we are talking about sentential logic here). Then the truth value of every formula is determined by that assignment. The $f$ you've defined is not a valuation at all.

Franklin Pezzuti Dyer

Jul 10, 2023 17:16

@lafinur I was referring more to the original problem. Suppose, for instance, that $\Gamma = \{x\to x\}$ where $x$ is a sentence symbol. Then $\Gamma' = \{\neg(x\to x)\}$. Is this consistent?

$Mathematics$ Discussion on question by A-Level Stu…

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Franklin Pezzuti Dyer

Apr 26, 2021 15:52

I highly recommend the book Inside Interesting Integrals by Paul Nahin :D

Game Development

Game development and other polite discussion. Game development...

Franklin Pezzuti Dyer

Feb 12, 2021 19:58

It's like geometry, but if you were using squishy objects rather than rigid ones

Franklin Pezzuti Dyer

Feb 12, 2021 19:42

Thanks! That video about unums is interesting, btw

Franklin Pezzuti Dyer

Feb 12, 2021 19:40

Hah not really, was just checking the room out

$Mathematics$ Mathematics

Associated with Math.SE; for both general discussion & math qu...

Franklin Pezzuti Dyer

Nov 7, 2020 15:31

howdy

Franklin Pezzuti Dyer

Jul 7, 2020 14:14

I recently went on a gleeful downloading spree and thought some of you self-learners might be interested

Franklin Pezzuti Dyer

Jul 7, 2020 14:14

(on account of COVID-19)

Franklin Pezzuti Dyer

Jul 7, 2020 14:14

By the way, did you guys know Springer is giving away a ton of free textbooks?

Franklin Pezzuti Dyer

Jul 7, 2020 14:13

@CalvinKhor Damn, I definitely don’t know enough about HA to answer that

Franklin Pezzuti Dyer

Jul 7, 2020 13:56

@CalvinKhor What’s the question? I don’t know much about HA but I’d be interested to give it a shot

Franklin Pezzuti Dyer

Jul 7, 2020 13:54

@CalvinKhor Doesn’t matter. They’re all connected anyways. :)

Franklin Pezzuti Dyer

Jul 7, 2020 13:53

Hello all, any interesting problems (not for exams) hereabouts?

Discussion on question by Franklin Pe…

Imported from a comment discussion on worldbuilding.stackexcha...

Franklin Pezzuti Dyer

Jul 22, 2020 12:46

@AlexP First of all, I’m not sure why one wouldn’t believe in evolutionary psychology. Second of all - since when has not believing in something made it a bad question topic? We (probably) don’t believe in mermaids or FTL travel, but there are plenty of “good” questions on this site about those topics.

Franklin Pezzuti Dyer

Jul 22, 2020 12:46

Regarding the downvotes: can someone please explain why they think this is a bad question? I don’t understand what makes this question “bad” and I would appreciate constructive criticism. Thanks!

Discussion on question by chasly - re…

Imported from a comment discussion on worldbuilding.stackexcha...

Franklin Pezzuti Dyer

Jul 19, 2020 05:52

Three cheers for Solipsism!

Discussion on answer by Radovan Garab…

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Franklin Pezzuti Dyer

Jul 10, 2020 12:54

@RadovanGarabik Note to self: as a rule of thumb, extracting protons from random objects is a bad idea. Beautiful answer. (+1)

Discussion on question by chasly from…

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Franklin Pezzuti Dyer

Jul 10, 2020 09:33

@chaslyfromUK You never said they automatically hate their stalkers. If anything, they would feel sorry for their stalkers, knowing exactly how they feel (by virtue of feeling the same way themselves, about someone else).

Franklin Pezzuti Dyer

Jul 10, 2020 09:33

Artificial insemination!

The Factory Floor

Main chat room for worldbuilding.stackexchange.com

Franklin Pezzuti Dyer

Jun 29, 2020 22:06

It’s definitely a story written in the spirit of Worldbuilding.

Franklin Pezzuti Dyer

Jun 29, 2020 22:05

Is anybody here familiar with the story Tlön, Uqbar, Orbius Tertius by Jorge Luis Borges?

Discussion on answer by wizzwizz4: Ar…

Imported from a comment discussion on philosophy.stackexchange...

Franklin Pezzuti Dyer

Jun 28, 2020 13:40

@Alex Your concern is based upon what I believe is a dubious assumption - the assumption that humans could potentially know enough about physics/chemistry/biology to create an arbitrarily accurate model of the human brain. I’d say it’s possible that the mind is so complex that humans can never fully “understand” it, since it is also the apparatus with which we do the “understanding.”

$Mathematics$ This is the Realm of Simply Beautiful…

Room for totally bored people to hang. Open discussions.

Frpzzd

Oct 6, 2018 18:52

I think only $\kappa=1$

Frpzzd

Oct 6, 2018 18:49

Oh wait. Do I have to prove this by axioms?

Frpzzd

Oct 6, 2018 18:49

:thonk:?

Frpzzd

Oct 6, 2018 18:48

0_0 whaaaaat?

Frpzzd

Oct 6, 2018 18:46

Sure!

Frpzzd

Oct 6, 2018 18:45

haha ok

Frpzzd

Oct 6, 2018 18:45

Frpzzd

Oct 6, 2018 18:45

Is that too much to ask of an integral?

Frpzzd

Oct 6, 2018 18:44

Oh, blah.

Frpzzd

Oct 6, 2018 18:44

Cool!

Frpzzd

Oct 6, 2018 18:43

@SimplyBeautifulArt Was that coherent? XD

Frpzzd

Oct 6, 2018 18:43

Cool corollary:
$$\int_0^{2\pi} \cos^{2n}(x+\lambda \sin(mx))dx=\frac{\pi}{2^{2n-2}}\binom{2n-1}{n}$$
if $m$ divides none of the numbers $2,4,...,2n$

Frpzzd

Oct 6, 2018 18:42

All good?

Frpzzd

Oct 6, 2018 18:42

Or something like that. XD

Frpzzd

Oct 6, 2018 18:41

That's a sum of roots of unity. It's equal to zero unless $m$ divides $n$.

Frpzzd

Oct 6, 2018 18:41

and then sum up the terms

Frpzzd

Oct 6, 2018 18:40

Factor out $e^{2\pi i n k/m}$

Frpzzd

Oct 6, 2018 18:40

Note that $f(\sin(mx))$ is unchanged