This is technically incorrect. While the square root is both the positive and the negative solution, the sqrt (√) operator results in the principal square root. For nonnegative numbers this is the nonnegative square root and more generalised for complex numbers it’s the square root that halves the complex phase.
Square root definition does not allow a negative number as an input. Only positives and zero.
Although it is possible to expand the definition to negative numbers, complex numbers, matrices…
So unless you followed a course where you thoroughly defined your expansion of sqrt, it only applies to real, positives number and zero. Its the thing with math, you have to define what you work with.
In my case, I did prep courses for entrance exam to engineering schools (something like in dead poet society but more modern), using sqrt(-1) somewhere would be an instant 0 mark. Like forgetting a unit in a physics test answer.
You’re missing the point. Math (especially advanced) is about precision and rigor. Writing sqrt of something negative is ambiguous. There are better ways of writing it as explained here https://lemmy.world/comment/18924227
Wolfram tells me
sqrt(-1) = iand it hasn’t lied to me yet.In what meaningful way is
i^2 = -1different fromsqrt(-1) = i?sqrt(-1) = ±i. The negative answer is also valid.
This is technically incorrect. While the square root is both the positive and the negative solution, the sqrt (√) operator results in the principal square root. For nonnegative numbers this is the nonnegative square root and more generalised for complex numbers it’s the square root that halves the complex phase.
Ah, good point; I’d forgotten that part.
Square root definition does not allow a negative number as an input. Only positives and zero. Although it is possible to expand the definition to negative numbers, complex numbers, matrices… So unless you followed a course where you thoroughly defined your expansion of sqrt, it only applies to real, positives number and zero. Its the thing with math, you have to define what you work with.
In my case, I did prep courses for entrance exam to engineering schools (something like in dead poet society but more modern), using sqrt(-1) somewhere would be an instant 0 mark. Like forgetting a unit in a physics test answer.
Sounds to me like this is exactly what the OP meme is referencing.
Basic math: square root only of positive numbers and 0.
Advanced math: square root of anything you want
You’re missing the point. Math (especially advanced) is about precision and rigor. Writing sqrt of something negative is ambiguous. There are better ways of writing it as explained here https://lemmy.world/comment/18924227
Except that yes, math is about precision and rigor, and yes, the square root of negative numbers is totally allowed (https://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers) and yes, math totally allows for statements with multiple solutions.
sin(x) = 0also has infinite solutions and yet it’s totally legal for x to make an equation like that.So what’s the square root of your mom then?
√∞ = ∞
You mean limit of sqrt(x) when x->+inf = +inf
Damn, hoisted by my own petard.
I’m very sorry you had to go through such stupid school tests, welcome to the real world.
sqrt(x)is just a shorthand forx^(1/2).