Which is the worst math debate: 0^0, sqrt(1), 0.999...=1, or 12/3(4)?

These are the most debated math topics on the Internet but which one is the worst?
(A) 0 to the 0th power=1 or undefined. No calculus limit here.
(B) sqrt(1) = 1 or both +-1?)
(C) 0.999...=1 or not?
(D) order of operations 12/3(4)=1 or 16

More than 28,000 viewers voted in my recent poll and now let's discuss what each debate is all about.
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#blackpenredpen #math

[blackpenredpen]

Can you solve x^ln(4)+x^ln(10)=x^ln(25)?

[thesnackbandit]

D is just intentionally bad notation. The others at least have some interesting mathematics behind them. So D is indeed the worst debate.

[o_s-]

D is the reason we don't use ÷ after elementary school

[brickbot.]

Half the comments are saying D is the worst debate, the other half are arguing about how it's really solved. ABC are just about forgotten

[NikkiTheViolist]

I definitely would say (d) is the worst because (a), (b), and (c) are all about defining different math concepts and people who don't understand the concepts, while (d) is about clarity and people being taught different things in school

[johnchessant]

230 – 220 × (1 ÷ 2)
You might not believe me, but the answer is actually 5!

[parttimegorilla]

Both Mathematicians and computer scientists agree that 0!=1

[Prismate]

B is the one I meet most often but D is just stupid

[Bstpwnage]

As a tutor, A is my least favorite. If only for the reason that I don't like saying anything "wrong." So when I bring up "Any number to the power 0 is 1" I always have to throw in "except 0, there's actually some disagreement on what that should be."

[yuujin]

B really seems almost more like a communication issue than a math issue. There is no question that 1 and -1 are both square roots of one. it's more that there is confusion over the fact that the square root function is only looking for the principle positive square root instead of all square roots.

[gamingbutnotreally]

D is on the verge of not being a math problem, it’s a problem of semantics not math. It’s closer to being a freaking English problem. I truly feel sorry to those that find problem D mathematically interesting / provocative because there are endless ACTUALLY interesting ideas to explore in mathematics.

[markus]

D is very weird as US Ppl give a different answer and always ride high on PEMDAS...

All over the rest of the world, the implied multiplication also implies paranthesis

[blanktom]

D is the least interesting as it's mostly a question on syntax. The people who say the answer is 1, generally do so because they view 3(4) as implied multiplication, which has been taught (by some) to have higher precedence than standard multiplication (using the "x" or "÷" symbols).
I wonder how the responses may change if we did some alterations to the question:
12/3(4)=?
or evaluate 12/3x where x = 4?
or what about:
12 ÷ 3π=? would you evaluate that as (12 ÷ 3) x π or 12 ÷ (3 x π)
I'm not arguing for one or the other, it's just that I can see how people would find it ambiguous and I can see an argument for both sides. But all in all, it's just not an interesting problem.

[anewman]

It's (D). The others at least require some mathematical thought. (D) is just dumb and is only an issue because people hate that particular division symbol and assume it means something that it does not.

[keej]

I think D is the worst because writing it in fraction form would clear any debate so I think it's more of a communication/notation problem than a debate really. I can't think of a single situation where I would rather write ÷ instead of just expressing division as a fraction.

[SourceEnginePlayer]

C is just straight up undebatable because its it is straight up literally 1

[ODDin]

I think the problem with D is that even with the same operation, it's usually implied that when the operation doesn't appear, it should be done first. e.g. when you write 12÷4a, you kinda want to do "4a" first. Obviously the whole thing with order of operations is just a convention. As a programmer, when I occasionally write math operations in the code, I often add parentheses which are technically redundant, just to make it clearer what is going on. e.g. I write var1+(var2*var3) instead of var1+var2*var3. They're technically the same, but the first is much easier to understand from a quick glance, and unlike what some people think, the point of writing things in math (and code) is to make it *easier* for other people to understand what they're reading.

As for the debates, personally I think the worst debate is C. Debates A, B and D are just about conventions. You can define these things however you want, it's just for the sake of convenience, there's no hidden meaning there. Like, you could define square root to be a function that returns pairs of values. It would be less convenient to work with, but nothing would break. C is the only debate that is actually about the *meaning* of something, that actually shows a fundamental misunderstanding of what real numbers are and of how series work.

[OptimusPhillip]

I think the issue with D is that there's disagreement about whether or not implicit multiplication takes priority over explicit division. I remember The How and Why of Mathematics made a couple videos about this debate, that I thought were really good.

[Alguem]

D is not a math problem it's a notation interpretation issue

So Why when it's 12/3X we interpret 3X as a number and not as 3 * X,



Prioritising implicit multiplication is more consistent

[Grecks]

For me as a math minor, the dumbest debate is (B). It's simple enough, easy to understand, not much room for debate. Functions must have unique values. Or a bit fancier: Functions can be considered as relations that are left-total, right-unique.

D) is actually worth debating imo, although it's only about notation. I also do not agree with the given resolution. For me, juxtaposition binds stronger than the division operator.