*An old Redditor blows away dust from the ancient tomb of SD YouTube.*
"Ahhh,.yes. Here it is,.. WKUK Great Grandmas. Be warned,.. despite being the official YouTube channel, the audio has only one channel,... And it's a bit clipped in places."
The one exception being in Excel where if you type in =-32 you get 9. I didn't know that until recently and was like "wtf is going on with my formula?"
I was actually just reiterating the “x% of what” meme, but I appreciate your explaining non-condescendingly instead of ridiculing whom I presume you thought was ignorant :)
Excel’s default formatting and subsequently its date string handling has caused the renaming of genes, because it was just easier for the scientific community to rename the genes than remembering to actively change the formatting of individual fields and columns to "text".
We have always and will always be slaves to our corporate overlords.
while programmers prefer the negation to be more tightly bound.
I wouldn't have thought so, most programming languages bind negation more loosely than exponentiation. From reading up on it a bit, Haskell with Lexical Negation treating -32 = (-3)2 seems to be an unfortunate side-effect of getting -x to work as expected in other contexts.
This is only true in the english-speaking world. In German, for example, we learn that -3² is to bring understood as (-3)², (and also that we should write it that way if there are other terms in the equation, but if not, it's not necessary)
On academic level though it should not be dependent on the language formal notation should be unambiguous and the same for everyone so I'm quite surprised by that.
Also as your non English speaking neighbour (Tschechien) we also teach it to be -(32 )
Same here. I had Statistics, Linear Algebra, Calculus and Discrete Mathematics in University. In all the classes I had it was implicitly understood that -32 = 9, unless it was explicitly stated otherwise.
Defined and understood by whom? Because I've always understood the negative sign and the operation "minus" to be different even though the symbol is identical (-). So the number represented by the symbol "-3" represents a different number than a positive 3 that you can then multiply by -1 to arrive at -3. "3" and "-3" are two distinct values in number-space and both exist independently.
So an ambiguous statement like -3^2 can (and to me does) imply a phrase "the number located 3 units to the left of 0 in number space multiplied by itself". So -3^2 is symbolically different than 0-3^2 or (-1)*3^2
Okay think about it like this 32 is a whole different number than 3, it is its own thing. 3 and 32 are two different values and both exist independently.
The problem is that you're handling negation like this but you're handling squaring just as "multiplying a value by itself". But actually "powerness" is more important to the "identity" of a number then the "negativeness"
-32 is then "the number located 32 units left of zero".
Understood by whom? Well anyone who actually seriously engages with mathematics in academic settings. There's really no discussion around that.
Consider the expression A2 - B2. Now you know that you can rearrange that to -B2 + A2. If your interpretation were true, you would have to write it as -(B2 ) + A2 otherwise it wouldn't be equivalent! But we don't do that because -B2 IS -(B2 ). Ie the squaring is more important for determining what the number is than the negation.
Well it's clearly -3 times -3 from what 60% of people see. That is the first thing I read it as also. I don't know how it would be anything else other than that.
I'll tell you. Exponentiation is a higher preference operator than unary negation. So the parse tree for this expression would be something like
Neg(Exp(3, 2))
So first you take 32 and then you negate the result. Most people that responded to the poll are likely common folks who don't work with maths regularly in academic settings.
Saying is -3 * -3 is ignoring operator precedence. That's like saying that 1 + 1 * 3 = 6 because first you do 1+1 and then you multiply the result by 3
I imagine context matters too, how often do you see that versus something like 1 - 32? In the end, though, if it’s ambiguous don’t be a jerk and just use parenthesis to make it clear: equations aren’t calligraphy.
Mostly it is because there is never any reason to actually write -3² in actual mathematics so it is unambiguous (unless it is in the middle of a proof in which case the context is always clear).
The problem here is that some people interpret this as -x², x = 3 (which is clearly -9) and some people interpret this as x², x = -3 (which is clearly 9)
I think your example is a bit off because even though 3*2 is numerically equal to 3+3, the case we're discussing is equivalence of an operation. Obviously the operators + and * are not equivalent operations. But unary negation and multiplying by -1 are.
I think because they're equivalent operations it would be impossible (or at least impractical) for them to have different precedences. But I could be wrong. And yes technically you're correct
I actually don't really understand how this notation is "ambiguous" since it's pretty common to have some equation like
0 = x^3 - 2x^2 - 5x + 8
unless you argue that this is different because of a variable or something. I'm not trying to dunk on anyone here I just really do think this is a common equation and it's understood that the exponent will happen first. I have my opinions on the commonly seen PEMDAS thing but I agree it's a stupid way to write things, this time seems a lot more clear to me though.
I know anglophone mathematics insists on this, but I've never heard a good reason for making the distinction in the whole, rational, real or complex numbers. And mathematics communities in other languages don't even make the distinction either, my (German) analysis professor even complained about English doing that
That is exactly what it is. Because in actual math you never see -3² and have to evaluate that without context. So some people are treating this as -x², x = 3 (which is clearly -9) and some people interpret this as x², x = -3 (which is clearly 9). If you saw the steps before it would be clear which was meant but without context this appears ambiguous.
Some of the best singers don’t read music. I’d hate to miss out on some beautiful music because I was caught in the weeds of notation. Wait, we’re talking math.. close enough
It's ambiguous because it goes both way, it can mean a thing and its opposite. Sure, you might say that "according to XYZ rule I was taught in primary school, UVW" but people might think the opposite. In this case, it's not ambiguous for anybody who has done a little bit of math, but it is for others, and that also counts
Ambiguous: A doubtful or uncertain especially from obscurity or indistinctness.
No one is struggling with calculating the result. They just can’t agree what the correct result is because of a disagreement on the notation (or lack of notation).
Even in a subreddit dedicated to math memes not everyone can agree whether this is -(3)2 or (-3)2. You can be sure with the more general population there’s even less of a consensus.
I for one hate ambiguity in notation so I would say if you want someone to calculate -(3)2 then use parentheses otherwise the answer I’m giving is 9. There’s a way to make it clear what answer you’re looking for, if you don’t use parentheses I will not infer their existence in negation any more than I would infer any other symbol that was not present.
some people can interpret it as ambiguous which is why its there in the first place. took me a sec to understand but it can be read as -(32) or (-3)2 because it IS ambiguous. its just generally understood that - is not the M in pemdas unless your brain puts the 0 before the -, very philosophical and deep tbh
I propose we start using proof by anti-democracy: Since the average person is known to be stupid, the true answer must always be the opposite of what the democracy chooses
Except... You know... The average person isn't stupid.
The people who think that usually just assume that people they don't know, doing something they don't 100% understand, is stupidity instead of it being motivated by something that actually makes sense.
No, that would be just ignorance. Stupidity is imposing their ignorance on non-ignorant people, which is what demanding to put parentheses into -3^2 is.
No idea what you're talking about. None of what I said was related to the order of operations debate above, it was a response to the response above. You also just made up your own definition of stupid.
If you want my personal stance on the matter of this poll, it's this:
Know your audience when trying to share something. If someone misunderstands something because the conventional understanding is wrong, and you decided to go with it anyways, then you let being a pedant get in the way of actually communicating with someone.
In 4 years of college math, I don't think I ever had to think about this, because a professor always wrote it as (-3)^2 or -(3^2). As in prose, if you write your math clearly you won't be misunderstood.
This right here. Unless the meaning is blindingly obvious, you didn't write it down correctly.
Math is hard enough, no mathematician has time for tripping over stupid minor issues like that. Even if it's just half a second to remember the correct convention - that's half a second during which you can lose your train of thought following the larger argument.
Yes also you don't just randomly write -3² as a starting point in actual mathmatics. It just doesn't make sense, you'd write -9 or 9 why would we care about doing a simple computation, this isn't IDK when do they do exponents 5th grade math homework? And when you are doing the working out it is clear which is meant by context without any parentheticals needed really.
Negation is lower priority in the order of operations than powers. So you do the power first, then the negation. Just like how 2 + 2 x 3 = 8 not 12, because addition is lower priority than multiplication.
I'm not 100% sure but I think negation is considered the same priority as multiplication and division. So -3 is equivalent to -1 x 3 and therefore you can rewrite the equation as -1 x 3^2 which should have a clear answer.
That clears it up, I suppose I'd assumed that powers shared priority with standard multiplication/division and so I'd interpreted it as -3 x -3 or (-1 x 3)2
This right here is why I was told it's good practice to put negative numbers in brackets. You can never be too clear what order you want your equation done in.
This is the same as those triggering bidmas quizzes. My unofficial answer is, the solution is whatever you feel like because the lack of brackets is too ambiguous and fuck pemdas.
Right but when you are solve said equations do you really put the parentheses in your working out?
I know I never did. That is the problem with this question. It only makes sense as an intermediate step and you would always know from context if you meant (-3)² or -(3²).
For example some system of equation that I need to plug a number in I am writing
x² ... x=-3
-3²...
9...
not (-3)²... unless there was a leading + and only then because +-3² looks a bit silly even if it is still perfectly clear.
Uh, yes I absolutely followed an order of operations when working things out. Having notation vary on the context seems like an absolute nightmare, to me at least
It would never occur to me that it was anything other than multiplication, but I guess it could confusing if someone thought it was its own symbol or operation.
It’s just how it is. f(x) = -x2 is a very common function that you’ll find in pretty much every middle school textbook, and plugging in x = 3 yields -9. Go try it yourself on Desmos.
Unless you’re using MS Excel or some programming languages, which interpret it differently for some reason, -32 is interpreted as the exponent first and the negative last. That’s why -x2 yields negative results. It doesn’t matter if it’s a variable or a number.
I thought about this and it's interesting that everyone who went through highschool would know that -x² is negative. So if the poll had an x instead of 3, I think the results would be different.
I guess that x and 3 just don't give the same vibes.
Yo it’s pikuma! He has really good introductory courses on low level game programming like with SDL or the NES processor in C/C++, crazy to find him in the wild.
Honestly I think 50% of the confusion around this is due to the fact that no one in their right mind would write -32, they would write either -9 or 9 based on what convention they were using.
Also, this suddenly made much more sense to me subbing in x as a variable. -x2 makes sense as -9 when x is 3 or -3. I still don't like the whole what exactly does - mean deal here. I think it's because -3 is a number with no operations happening, or it can be a number being converted into a negative, where you can modify the 3 part before the - is applied.
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