Min and max are elementary functions?!

A certain web site lists min and max as being elementary functions.

Before trying to explain to them why their classification of min and max as
elementary was wrong, I decided to ask here:

How would you explain to them what's wrong with that classification?

Of course, I'm assuming that you agree that min and max are not elementary.
But if you think that, somehow, they can legitimately be called elementary,
please tell me why. I expect that the people running the web site will say
that

min(a, b) = 1/2 (a + b - sqrt((a - b)^2))

and

max(a, b) = 1/2 (a + b + sqrt((a - b)^2))

justify classifying min and max as elementary. But of course, for those two
identities to be correct, "sqrt" must be the _principal_ branch. And
there's the rub...

David
.

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