04/05/2011, 03:22 AM

I have often woundered myself about superroots and superlogs, and as to how one might define:

a[-b]c and a[b]-c.

I mean, could we have multiple definitions of these for b=4, such as:

1/(e[4]b) or cos(b*pi/4)+sin(b*pi/4) in radians.

I mean, do our definitions HAVE to be logically consistant, could we not just use the definition which suits us in whatever particular circumstance?

a[-b]c and a[b]-c.

I mean, could we have multiple definitions of these for b=4, such as:

1/(e[4]b) or cos(b*pi/4)+sin(b*pi/4) in radians.

I mean, do our definitions HAVE to be logically consistant, could we not just use the definition which suits us in whatever particular circumstance?