I have always been annoyed by the statement that sqrt(-1) = i.
Note: I'm perfectly fine with the assertion that i^2 = -1.
sqrt(1) = -1. We're either constraining the answer to positive numbers or we're not.
piecewise function definitions are a thing though, like the abs function for instance
abs(x) = x, for all positive x
abs(x) = -x, for all negative x
sqrt(x) = positive y, for all positive x
sqrt(x) = i * sqrt(-x), for all negative x
I also find arctan really weird, because it only works if you fiddle with the domain (yet it clearly does exist, and is useful)
I enjoy the unpleasant feeling I get when I realise that all maths is made up!
abs can be defined for the whole complex plane though (the square root of the sum of the square of the real and imaginary components) i.e.:abs(a + bi) = sqrt(a^2 + b^2)
@Eric Gerlach I... guess, but I'd imagine there are less violent ways to feel that control.
Maybe that's just me.
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Fortunately fountain pen ink is water soluble so it often washes right out if you get to it immediately.
Thank God it wasn't my Baystate Blue.
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Kevin Davy
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