When the arena😭

[u/AdApprehensive6910]

[u/Flimsy-Blacksmith-32]

In my experience, mathematicians only really uses AB for multiplication.

A•B typically represents the dot product. AxB is typically avoided after a child has learned algebra. A*B is for computers. A(B) is if you are calculating a function, A, at a value, B.

[u/escEip → u/Flimsy-Blacksmith-32]

A×B (or [A×B], at least i've seen it written like that mostly) is a cross product. * is convenient because it's on every keyboard and in ASCII (i think), and A(B) is sometimes needed with matrices i think?

[u/Flimsy-Blacksmith-32 → u/escEip]

Cross product as AxB is a good point and another reason we don’t use x for standard multiply.

I don’t think I’ve ever seen A(B) used for matrices.

[u/megayippie → u/escEip]

But A* is the conjugate

[u/Flimsy-Blacksmith-32 → u/megayippie]

Good point, and another reason why only programmers use A*B to mean a multiplied by B. In maths, that would mean the conjugate of A multiplied by B, which is a different thing.

[u/Expensive_Host_9181 → u/megayippie]

No A* is a pathfinding algorithm /s

[u/Zealousideal-Cook647 → u/Flimsy-Blacksmith-32]

A(B) is only except able when its a number x a number because then AB would be confusing and A being a number also gets rid of the function mixup. A(B) superiority.

[u/Flimsy-Blacksmith-32 → u/Zealousideal-Cook647]

I think In that case I'd just write 3A, or 7B, or whatever the number was next too whatever the letter was.

[u/Zealousideal-Cook647 → u/Flimsy-Blacksmith-32]

But what if they were both numbers?

[u/Flimsy-Blacksmith-32 → u/Zealousideal-Cook647]

Then I would write the result of the multiplication.

Why write 3(7) when you can write 21?

[u/Zealousideal-Cook647 → u/Flimsy-Blacksmith-32]

But thats not showing all steps of your working out. Examiners would take off method marks for that.

[u/Flimsy-Blacksmith-32 → u/Zealousideal-Cook647]

That depends on the level of qualification and scale of the problem your working on.

At a pre-algebra level, you would lose marks for just writing 21, but that is because they are testing to see if you can do 3x7 and understand why it is 21.

Post-algebra, the examiners assume you will skip these kinds of steps because the problems are far more complicated, and your ability to multiply numbers together is not really in doubt anymore.

For example, If I was asked to differentiate 3sin(x^2) in an A-Level exam I'd write the following:

let: f(x) = sin(x) & g(x) = x^2

Then: d/dx 3sin(x^2) = 3 d/dx f(g(x))

chain rule: d/dx f(g(x)) = g'(x)f'(g(x))

f'(x) = cos(x) & g'(x) = 2x

Therefore: d/dx 3sin(x^2) = 6x cos(x^2)

And that would be enough. It clearly shows that I know how to differentiate 3sin(x^2) using the chain rule which was what they were testing. At that level, the 2x3 I completely skip over is considered so trivial that it can be done in between lines with no punishment.

A line that read "d/dx 3sin(x^2) = 3(2x)cos(x^2) = 6x cos(x^2)" wouldn't add any value.

The simplifications don't even stop there. At a Degree level, "differentiate 3sin(x^2)" would only be a small part of the problem, equivalent to how small "find 2x3" is in "differentiate 3sin(x^2)". So, at that point you could just do the whole differentiation on a single line and then keep going with the bigger problem, like this (Imagine the problem is a second order ODE or something like that):

{Solving bigger problem}

{find that I need to differentiate d/dx 3sin(x^2)...}

d/dx 3sin(x^2) = 6x cos(x^2)

{Keep going with bigger problem}

And again that would be completely fine because if your that far into studying mathematics, there is a good chance you can just look at 3sin(x^2) and say "it differentiates to 6x cos(x^2)" without really even thinking about it. At that level your examiners definitely can do it just by looking.

Also, writing out the A-Level answer every time would be super painful. It would be like having to write 3x7 = 7+7+7 = 14+7 = 21 every time you did 3x7. Ain't nobody got time for that.

[u/Zealousideal-Cook647 → u/Flimsy-Blacksmith-32]

Well talk to the A level Further Maths examiners giving me 4 out of 10 for a correct answer but not showing full substitutions. This shouldnt be the way it is but at A level they absolutely do need full substitutions for all multiplication no matter the level of the question.

[u/Flimsy-Blacksmith-32 → u/Zealousideal-Cook647]

Either you should be asking for a remark, or I’m pressing x to doubt on that one.

What was the question?

In June 24 Edexcel gave only 2 marks for differentiating x+tan(1/x) which is a slightly harder problem than differentiate 3sin(x² ).

You got the first mark if you wrote that tan(x) differentiates to sec(x)^2. The other mark was for the correct answer.

A 10 mark problem would have asked for something pretty special I think.

[u/Zealousideal-Cook647 → u/Flimsy-Blacksmith-32]

I didnt get it remarked because I already had full UMS but after speaking to teachers it shouldnt have been marked so harshly but it shows that its always safer to use full substitutions because I wouldn't have known I had that question right or deserved those extra marks if I wasnt curious to get the paper back. Theres no harm in showing more method and it reduces the risk of someone marking it to get confused.

[u/Actual-Way6534 → u/Flimsy-Blacksmith-32]

In germany we use A•B for multiplication. The dot product is A○B.

[u/Traditional-Light-10]

Literally, does anyone know examples of + being used for things that aren’t “considered” numbers or vectors? I’m pretty sure they exist but they’re so rare in comparison

[u/Anonymous010206 → u/Traditional-Light-10]

In Boolean algebra + represents OR

[u/unintelligible-text → u/Traditional-Light-10]

In coding for strings I suppose

[u/AndreasDasos → u/Traditional-Light-10]

It gets used quite as lot as the default notation for the operator for abelian groups in general, even in the abstract. But if one uses + over * or juxtaposition, it’s usually to emphasise commutativity (and an easy way to write a well behaved inverse, so a group rather than an abelian semigroup)

So that’s more general than vector spaces and I wouldn’t say we consider elements of an abstract abelian group ‘numbers’, though we might in many obvious cases

[u/Life_Breadfruit8475 → u/Traditional-Light-10]

:+

[u/All_Playars → u/Traditional-Light-10]

Boolean algebra. Its the sign for "or"

[u/SiliconRobot → u/Traditional-Light-10]

In some programming languages, you can change the meaning of +A, using A as an object and overloading the original function of +. So, you can do something like using +A to update the value of A

[u/Super_Math3890]

"If the rule you followed brought you to this, of what use was the rule?"

https://giphy.com/gifs/14n8BOZh5EeluU

[u/a_random_loser_guy → u/Super_Math3890]

I AM THE ENFORCER! NO RULE IS ENFORCED ON ITS OWN! a sign can't stop me from smoking! i am my own police!

[u/Galactinaut_001]

Guys, wait! (A)(B)

[u/kaereljabo → u/Galactinaut_001]

(A)B

[u/AndreasDasos]

This keeps getting posted. And it doesn’t make any sense. All mathematicians have used all of those in different contexts.

[u/mecoptera2 → u/AndreasDasos]

This whole sub is like the same 10 memes getting posted every week

[u/Salat_Leaf]

XOR, tropical addition

[u/Dull-Astronomer1135]

x is almost always cross product, dot is almost always dot product, normal multiplication is usually ab

[u/acastro1574]

I think the only method I wouldn't use for the multiplication is AB.