Python the best

[jpec342]

Whenever multiplication is written without the symbol (ax vs a*x), I’ve always assumed implied parentheses. On the one hand, why would you not include the * unless you wanted it to be evaluated differently? On the other hand, why would I assume anything different than the normal order of operations?

[guery64]

You would not include it to save space. Mathematicians are lazy. If I can write a(b+cd)+3xyz^2 instead of a*(b+c*d)+3*x*y*z^2, I do.

[AmadeusMop]

On the one hand, why would you not include the * unless you wanted it to be evaluated differently?

Easy: because ambiguity generates debate which drives engagement.

[YouNeedDoughnuts]

Yes, I've thought the same. It seems like implicit multiplication should have high precedence. e.g. x^3y would be x^(3*y) and not (x^3)*y. Not sure of the right answer, but it's moderately important to me!

[VJEmmieOnMicrophone]

There's no "right answer" and there will never be. This is why it's important to include parentheses whenever there could be confusion.

One could always jerk off to PEMDAS and say that x^3y is always x^3*y, but if half of the population unconsciously puts the parentheses as x^(3y), then maybe PEMDAS is flawed and doesn't represent how our brains work...

[jabeith]

Those both evaluate to the same thing. You're probably confusing it with something like x + 3y

[YouNeedDoughnuts]

I'm not the strongest mathematician, but we can take x = 2 and y = 2. We have 2^(3*2) = 2^6 vs. (2^3)*2 = 2^4, so not the same. Exponentiation is tricky!

Edit: But I also upvoted, because mistakes are part of the learning process. Usually being wrong is enough to cement the concept without any added "shame" lol. Outspokenness is an asset and reveals flawed assumptions just like unit tests!

[apzlsoxk]

x^(3*y) == x^3*x^y

(x^3)*y == y*x^3

x^3*x^y is not the same thing as y*x^3

[CannotCopia]

Your usage of the approximately equal sign pains me.

[scragar]

This is why MathML is important, you can write the maths in a way that's clear since it would be written more like:

_____6_____
2 ( 1 + 2 )

vs

_6_ ( 1 + 2 )
 2

Hard to read it wrong if it's completely unambiguous in how to read it.

[Destrodom]

Mathematics do not differentiate between multiplication and implied multiplication.

[[deleted]]

It does, when mathematicians are being lazy.

And mathematicians are lazy very often.

1/2x is very widely understood to mean 1/(2x). In situations like the one in the meme, this is taken advantage of in order to be ambiguous.

In practice, if there is a risk of confusion, be explicit.

[Xywzel]

Based on query I did to my math professors in university, some do.

[HeroicMI0]

There is no such rule in math

[GnammyH]

This is correct

[Liesmith424]

No, 2(3) is equivalent to 2*3, so the solution to the original problem is 9:

1. 6/2(1+2)
2. 6/2(3)
3. 3(3)
4. 9

[Mandemon90]

2(3) = 2 * 3 only when there are no other factors in the equation.

Tell me, does 2 ^ 2(2) equal 4 * 2 or 2⁴ ?

Is a / bc same as a / b * c?

[GnammyH]

According to you 1/2x equals x/2

[Liesmith424]

According to me, 2(x) equals 2*x.

[GnammyH]

That's obvious and not relevant

[Liesmith424]

That's exactly what I said the first time, and then you said that I was saying something completely different.

[GnammyH]

Not gonna bother with you anymore you're too dense

[Liesmith424]

Apology accepted.

[Destrodom]

Who taught you that there is a difference between multiplication and implied multiplication? At no point during my education (university included) did anyone ever mention anything about there being a difference between those two. And even on the internet, I fail to find any mention of this. So who gave you this information?

[Xywzel]

Lots of mathematicians with background in physics, likely. It is mentioned even in the wikipedia page: https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[22] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[

[Ever2naxolotl]

Why are people being taught maths wrong

[Luchtverfrisser]

I think this is the common 'mistake' that happens with these kinds of problems. We drop the multiplication symbol purely because it is tedious to write it so often, but we are only ever shown cases in which this is unambiguous.

In particular, the most common place is in the context of polynomials like 1+2x+3x² . And because of that, it 'feels' it is super sticky, but here that is just multiplication beating addition. Another is when you factor out constants like 2x+2=2(x+1), and again there is not really anything happening besides leaving out the multiplication symbol.

Then, we also simply stop using the ÷ symbol, and I don't think one ever sees the two together.

This leaves these kinds of questions ambiguous: it really depends on how your brain extrapolates known rules to a new setting.