1) Halle all continuous functions g: (0, + infinity) -> R such that g (x ^ y) = g (x) ^ g (y) for all x, y.
2) Show a discontinuous function g: (0, + infinity) -> R such that g (x ^ y) = g (x) ^ g (y) for all x, y.
("^", as always, means "raised to the").
[Since the comments on this post have strayed from the initial theme and have been immersed in the discussion of 0 ^ 0, I decided to add the entry label Irrefutable but resisted, with which designate entries which speaks of the statement "0 ^ 0 = 1." I also observed that, at the time of this writing, 2/15/1911, the second Part of the problem is still no resolution.]
0 comments:
Post a Comment