5 ms·

"inverse" has a very specific meaning: inverse(x) * x = 1 x^2 * x != 1 for any x other than 1. So no, x^2 is not the inverse of sqrt(x)

tczMUFlmoNk 2y ago
But sqrt · square = 1, where "sqrt: R⁺ → R⁺" is the square root operation, "square: R⁺ → R⁺" is the squaring operation, "1: R⁺ → R⁺" is the identity operation, and (·) is function composition: i.e., working in the monoid of functions R⁺ → R⁺. So x² and sqrt(x), as elements of R, are not inverses, but sqrt and square, as elements of R⁺ → R⁺, are. It depends on how you parse the phrase "fast inverse square root".
- xigoi 2y ago
  This is true, but interpreting it one way is clearly absurd (nobody would call a square the “inverse square root”), which implicates that the other meaning was intended.
quietbritishjim 2y ago
No. "inverse" has a very specific meaning: the operation that undoes whatever operation you're talking about. https://en.m.wikipedia.org/wiki/Inverse_function https://en.m.wikipedia.org/wiki/Inverse_function The inverse of multiplying by 3 is dividing by 3, and vice-versa. The inverse of squaring is squart root, and vice-versa. The inverse of a number or other element (rather than an operation / function) means whatever number would form the inverse if you use it with whatever binary operation you're talking about. So the additive inverse of 3 is –3, the inverse of "rotate clockwise 90 degrees" in the group of geometric operations is "rotate anticlockwise 90 degrees", and the multiplicative inverse of 3 is 1/3. Saying "the inverse of 3" to mean 1/3, i.e. its multiplicative inverse, is sloppy but acceptable so long as everyone knows what you mean (and it's fairly common). Saying "the inverse square root" to mean 1/square root is just wrong.
- sunk1st 2y ago
  Is it acceptable to use the imperative? That is, to say: “Now, invert the element”. Or should it always be, “take the inverse of …”?

tczMUFlmoNk 2y ago

But sqrt · square = 1, where "sqrt: R⁺ → R⁺" is the square root operation, "square: R⁺ → R⁺" is the squaring operation, "1: R⁺ → R⁺" is the identity operation, and (·) is function composition: i.e., working in the monoid of functions R⁺ → R⁺. So x² and sqrt(x), as elements of R, are not inverses, but sqrt and square, as elements of R⁺ → R⁺, are. It depends on how you parse the phrase "fast inverse square root".

xigoi 2y ago
This is true, but interpreting it one way is clearly absurd (nobody would call a square the “inverse square root”), which implicates that the other meaning was intended.

quietbritishjim 2y ago

No. "inverse" has a very specific meaning: the operation that undoes whatever operation you're talking about. https://en.m.wikipedia.org/wiki/Inverse_function https://en.m.wikipedia.org/wiki/Inverse_function The inverse of multiplying by 3 is dividing by 3, and vice-versa. The inverse of squaring is squart root, and vice-versa. The inverse of a number or other element (rather than an operation / function) means whatever number would form the inverse if you use it with whatever binary operation you're talking about. So the additive inverse of 3 is –3, the inverse of "rotate clockwise 90 degrees" in the group of geometric operations is "rotate anticlockwise 90 degrees", and the multiplicative inverse of 3 is 1/3. Saying "the inverse of 3" to mean 1/3, i.e. its multiplicative inverse, is sloppy but acceptable so long as everyone knows what you mean (and it's fairly common). Saying "the inverse square root" to mean 1/square root is just wrong.

sunk1st 2y ago
Is it acceptable to use the imperative? That is, to say: “Now, invert the element”. Or should it always be, “take the inverse of …”?