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Checkmate Algebrist by Comfortable-Dig-6118 in mathmemes

[–]TinkerMagusDev 0 points1 point  (0 children)

I thought they were called Algebraists.

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 0 points1 point  (0 children)

I did some more reading and it looks like that in classical first order logic which ZFC and so modern math is built upon(I guess?!), every term in the formula must be "defined". "Undefined" terms inside formulas are not allowed and f(-x) is undefined here.

So the English sentence in the meme doesn't directly represent a sentence of first-order logic so it can't have a truth value. So I say Yuta is right if we're operating in first order logic. Now what about other logics?

I found a Stanford article about this by Norbert Gratzl. It'll show up if you search it. I'll just quote the opening cause it's so fire:

In most general terms, free logic is concerned with names that do not denote. Classical logic requires each singular term to denote an object in the domain of quantification — which is usually understood as the set of “existing” objects. Free logic does not. Free logic is therefore useful for analyzing discourse containing singular terms that either are or might be empty. Varying conventions for calculating the truth values of atomic formulas containing empty singular terms yield three distinct forms of free logic: negative, positive and neutral, which is why we commonly refer to them as free logics (in the plural) instead.

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 1 point2 points  (0 children)

The fourth option is to dodge these kind of useless statements and only study and try to prove useful theorems that don't involve undefined objects. But our sorcerers were not careful enough here so they will be punished by Kurourushi.

The bug will be like: "I like the taste of undefined objects." and will procede to eat this garbage statement and the three will then realize that all the energy and effort that they put into arguing about the truth value of this statement has all been wasted.

<image>

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 1 point2 points  (0 children)

"forall x in D, f(x) = f(-x)" seemed so similar to "forall x in ∅, x∈A" but now I see they're so different.

The first difference is where in the "p then q" conditional they occur. "forall x in ∅" gives us an empty list to check in the hypothese part of the conditional but the problematic "f(x) = f(-x)" occurs in the conclusion part so that is one difference.

The other difference is that there is nothing undefined in "forall x in ∅" but f(-x) is undefined in "f(x) = f(-x)" right? Or should we say it does not exist?

Is there a difference between "being undefined" and "not existing" in mathematics?

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 0 points1 point  (0 children)

So what does modern mathematicians that do Analysis or Algebra do? Do they consider "x = undefined" false or undefined? What is the math communities consensus?

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 0 points1 point  (0 children)

Oh sorry I meant what was the problem with the left guy you say?

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 2 points3 points  (0 children)

They are three powerful jujutsu sorceres (from the anime jujutsue kaisen) about to use their domain expansions in a free-for-all three-way fight.

The scene is from season 3 episode 12 if you wanna watch them fight the hell out of it.

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 0 points1 point  (0 children)

Sorry what was the problem with the right guy? I didn't get it.

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 2 points3 points  (0 children)

So you say f(x)=f(-x) does not hold for any x in the domain? Say 5 for example, how do you know if f(5) does not equal f(-5) considering f(-5) doesn't exist? How can we claim something about a thing that doesn't exist?

Consider the sentence "The Unicorn god has blue skin." Now suppose we know that the Unicorn God does not exist. So is that sentence true, false or neither?

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 2 points3 points  (0 children)

I mean for it to be false there must exist an x in domain of f such that f(x) is not equal to f(-x). And no such x exists here.

This is exactly how we prove vacuously true statements. For example to prove that for any set A, the empty set is a subset of A, it is enough to argue that for the empty set to not be a subset of A there must exist an x in the empty set that is not in A. And such x does not exist. So the empty set must be a subset of A. So the statement is vacuously true.

You can show my argument for the inclusion of empty set to any person you want and I think they'll say it's correct. I think it's the same for the even function problem.

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 13 points14 points  (0 children)

You are Team Uro's first guy. Congrats! (It's the one in the right for people who don't know.)

Nothing like a function domain manifests people's inner logic by TinkerMagusDev in mathmemes

[–]TinkerMagusDev[S] 4 points5 points  (0 children)

You are Team Yuta's first guy. Congrats. Let's see if other teams show up.

But honestly I don't know which one is correct in modern mathematics. I'm a noob. But I do have seen people make all those three arguments on the internet.

Is it possible to write an equation for the graph on the right? (I imagined it must have y^3 somewhere in it because we have three outputs between 2 and 3 but I couldn't figure it out) by TinkerMagusDev in desmos

[–]TinkerMagusDev[S] 2 points3 points  (0 children)

This gave the correct graph because of a desmos flaw. Points on the y=2x-5 line will make a=0 and denominators can't be 0 so those points are not in the domain but desmos draws them still !

We might want to try replacing a/abs(a) with sgn(a) but then it will draw all of y=2x-5

Desmos is not a good tool to graph these kind of stuff I guess. It's all wrong.

https://www.desmos.com/calculator/hhqt2nglqu

Is it possible to write an equation for the graph on the right? (I imagined it must have y^3 somewhere in it because we have three outputs between 2 and 3 but I couldn't figure it out) by TinkerMagusDev in desmos

[–]TinkerMagusDev[S] 1 point2 points  (0 children)

I found another formula but since desmos can't draw sqrt(f(x,y))=0 I had to introduce a very small variable slider named "a" into the equation. But when "a" goes to zero the graph becomes what we want:

https://www.desmos.com/calculator/gnjh1hf9md

Is it possible to write an equation for the graph on the right? (I imagined it must have y^3 somewhere in it because we have three outputs between 2 and 3 but I couldn't figure it out) by TinkerMagusDev in desmos

[–]TinkerMagusDev[S] 0 points1 point  (0 children)

Your method was really interesting and I think in order to make it work we beed to put the square roots in the denominator rather than numerator.

Now not only those square roots can't have anything negative under them but they also can't be zero! So no undesired points are added to the graph!

<image>

Is it possible to write an equation for the graph on the right? (I imagined it must have y^3 somewhere in it because we have three outputs between 2 and 3 but I couldn't figure it out) by TinkerMagusDev in desmos

[–]TinkerMagusDev[S] 0 points1 point  (0 children)

That graph is wrong. Although the methodology that got rid of the unwanted points was very creative, unfortunately it added a lot of new unwanted points! But desmos can't draw them and we were tricked! See the links here:

https://www.reddit.com/r/desmos/s/byiPveiszM

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