3 ms·
It's not a simplification, it's wrong. Sqrt(square(x)) equals abs(x).
by contubernio 7mo ago
It's not a simplification, it's wrong. Sqrt(square(x)) equals abs(x).
- MForster 7mo agoIt also equals x with appropriate assumptions (x > 0).
- exe34 7mo agoso there's an unconditionally correct answer (it's also equal to abs(x) for x>0), and then there is an answer that is only correct for half the domain, which requires an additional assumption.
- crubier 7mo agosqrt(square(i)) != abs(i) So no, it’s not unconditionally correct either.
- notarget137 7mo agoWell, then sin(x) = x if x is infinitely small
- kccqzy 7mo ago> Assuming[x == 0, Simplify[Sin[x] == x]] Mathematica returns True. And any middle schooler will also tell you it's true. The only reasonable interpretation of "infinitely small" is that it's zero.
- oh_my_goodness 7mo agoNot in general. As people have pointed out elsewhere, it's true if x is real. That isn't always a helpful assumption. (When x is real you can plug that assumption into Mathematica. Then Mathematica should agree with you.) But consider sqrt(i) = sqrt(exp(i\pi/2)). That's exp(i\pi/4). Your rule would give 1 as the answer. It's not helpful for a serious math system to give that answer to this problem. When I square 1 I don't get i.