Well, you could assert that there is no discussion, but you are apparently
wrong.
sqrt has 2 values except at zero. (in the complex plane, or on the real
line).
for example, sqrt(9) is the set {-3,3} . That is how it is extended.
and sqrt(1) is {-1,1}.
Is it true that 1 is equal to {-1,1} ?
Now you could insist that sqrt() means only one of the roots. Etc for
other roots and for
other domains. But you would have to fill in what Etc means.
What do you suppose is going on at WRI, and with Maxima, each refusing to
do this?
(you do know that dividing by x and then letting x be zero is
problematical in general.)
On Monday, December 15, 2014 2:29:54 PM UTC-8, Jeroen Demeyer wrote:
>
> On 2014-12-15 20:47, rjf wrote:
> > Maybe it's an appropriate response?
> No, it's not.
>
> > Note that dividing both sides by sqrt(x) gives you sqrt(x)=1.
> > So the solution is x=1 maybe.
> > But x=0 is obviously a solution too.
> I think there is absolutely no discussion that the solution set of
> [sqrt(x) == x] is the set {0,1}.
> It doesn't matter how you extend the sqrt() function to the complex
> plane...
>
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