@Tata-ps4gy
I'll teach my children to subtract base six numbers with an arrow. You are a genius bro
@georgelaing2578
What an interesting idea! That the appearance of a symbol should share traits of its meaning! Once again, a unique video!
@papalyosha
Egyptian symbols for abstraction was asymmetric: it was legs that goes from the number: 𓂻 or 𓂽. It similar to arrows that you suggest. Egyptians usually write from right to left. Then 𓂽 would mean "subtraction". But sometimes they write from left to right. In this case 𓂻 would mean subtraction.
@jank.7781
It's good to hear that I'm not the only person who is obsessed with mathematical notation. I found your arrow notation for subtraction really intuitive! I always found a bit weird that the notation for the formula of a vector from A to B first mentions B and then A.
@theevilcottonball
I never flipped the vector then moved it head to tail and then walked both vectors to get the result. In the case of A-B I simply walked B backwards then forward to A. B -> A notation already kind of exists , denoting the vector from B to A but the arrow is usually on top above both letters. Denoting non-commutative operations with asymmetric operators, is already kind of an idea that is around, but many operators do not follow this rule. Connecting subtraction with invariants is the new thing I was introduced to here.
@seanscon
ah, a operator to designate Final - initial. I like this.
@sullivan3503
This is so good! I always struggled with remembering that the difference between two vectors is final minus initial. With subtraction having an arrow notation this would never have been an issue!
@blue5659
Yes, please do a video on the unified framework
@completo3172
very nice! representing -a as (a -> 0) feels correct, as a and (a -> 0) cancelling out is greatly announced by the notation: a + (a -> 0) = 0 also, for vectors one can also have the classic way of substracting vectors purely with the notation: A - B = A + (B -> 0) -B = B -> 0 also gives notational insight on why -B flips the vector around.
@forasago
I already loved vector subtraction before and you made it even more appealing. Thanks!
@harrytsang1501
The arrow notation clicks very well for vectors
@AloisMahdal
I would love to see a video from you about the Eric Hehner's system!
@zacharyvanderklippe5855
I was so convinced you had the arrow pointing the wrong way, i almost complained about it. The T shirt example really worked for me to understand that it's subtraction that is unintuitive, and this is largely because the operands are actually on the wrong sides of the operator.
@lazergenix
Using an arrow for subtraction is just so obvious, now that I've seen this notation I will try use this for vectors. Great video, this should be shown in schools ❤
@Azyo64
Really like the concept! But I think that the simple arrow isn't the good operator to use (already used too much). Instead, I would prefer the -+ operator "minus plus" arrow that neatly reverse into the +- "plus minus" arrow. And what is really cool about it is that it (almost) doesn't change the original meaning of the binary plus (A+B) and unitary minus (-B) operators: A - B = A + -B = A +- B = B -+ A = B- + A So we get that the binary + combine with the unitary - to form +-, and then we can reverse it -+, but when decomposing it again the unitary - get to the right side of the symbole B- (so maybe it would imply that we can put the unitary minus on both side ? It would only be (very) confusing if we kept the binary -. Probably say to not use B- but B-+A is ok). For the chaining, the best way would probably then be: A +- B +- C = A + -B + -C = A - B - C C -+ B -+ A = C- + B- + A = A - B - C (is consistent) It is the way that make the most sense considering the decomposition, but would be different from logic where C => B => A = C => B ∧ B => A and gives C => A (but then the B doesn't serve anything to the arithmetic operation). But if we consider: A +- B -+ C = A + -B- +C = A + B + C ??? Whatever is the case, the chaining must only go in one direction, just like the regular binary minus forces you to. So maybe just use the unitary left minus -B (and no binary minus), and combine it to a binary plus if it make sense? (A + -B -> A +- B and -B + A -> B -+ A) edit note: apparently -text- makes strike-through text , zero-width space to the rescue.
@Omeomeom
you convinced me bro they should change it. every math class is taught with this from now on
@BleachWizz
11:43 - i'm going to be honest i liked that backward arrow more than the arrow, it allows you to write the terms in the same order.
@nikosaarinen3258
I would love to see a video on Eric Rehners system
@LeetMath
what if we used an arrow with a bar through it? then ( A —> B ) in general gives you the mathematical object that when applied to A, gives you B. then you can put the operation that you are involving, in the middle. so subtraction would be arrow with a plus sign in the middle. but if you did an arrow with a multiplication symbol in it, then ( A -x-> B ) gives you B/A = A^-1 * B in geometry you could have the arrow operation give you objects that are not the same type as the original objects. you could have points P, Q, and have the arrow with a ‘v’ return the vector that takes P to Q. P -v-> Q = u, then u(P) = P + u = Q. you could have u -r-> v = R, give you a rotor-scalar that takes the vector u to v. if you don't have complex numbers, then it doesn't make sense to talk about multiplying vectors and it doesnt make sense to talk of the 'inverse' of u, but you can say that R(u)=v. you could have u -f-> v which returns a unique reflection transformation that takes u to v, and you could do the same with two points, P-f->Q giving a reflection transformation. you could have this work with tuples as well, provided there is a unique object. you could take two quadrilaterals of points (A,B,C,D) -p-> (F,G,H,J) = P and return a unique projection operation. this also avoids looking as much like a logical implication symbol.
@azai.mp4