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What they actually see:
convolution
cross product
dot product
multiplicationNo. If a is a scalar, which it clearly is, it’s all multiplication. And there is no reason to use any of the first three. We say “three apples”, not “three x apples”.
hurr durr maybe it’s a vector in ℝ
Tropical geometers: a^3
a+a+a
0a0 + 3a1
a, three times.
madness. How am I supposed to know if 36 = 36 or 36 = 8?
Numbers are all made up stuff, and they’re all the same. Here, lemme prove it; let a=b, and…
a² = ab // multiplying both sides by "a" 2a² = a²+ab // adding a² to both sides 2a²-2ab = a²-ab // subtracting 2ab from both sides 2(a²-ab) = 1(a²-ab) // isolating (a²-ab) 2 = 1 // dividing both sides by (a²-ab)From there you can prove any number is any number. 36=36 or 36=8 or 36=π.
the trick
If a=b, you can’t divide both sides by (a²-ab), because it’s a division by zero.
Lots of zeros in that due to a=b (before looking at the spoiler text)
Bingo. The whole “a=b” is just a distraction to hide it, otherwise as soon as you hit the third step you cancel both out, and end with 0=0.
