10/23/2007, 04:22 AM
This has probably been addressed already, but...
we have the rules for exponentiation like
e^x*e^y = e^(x+y) and
(e^x)^y = e^(x*y) and
(e^x)^(e^y) = e^(xe^y)
so for tetration we might expect
(where ^xe means e tetrated to x) (and * means multiplication)
^xe*^ye = ^(x*y)e
^y(^xe) = ^(x^y)e
^(^ye)(^xe) = ^(x^(^ye))e
translated:
e tetrated to x times y tetrated to e = (x times y) tetrated to e
(e tetrated to x) tetrated to y = e tetrated to (x to the y)
(e tetrated to x) tetrated to (e tetrated to y) = e tetrated to (x to the (e tetrated to y))
does this sound reasonable?
we have the rules for exponentiation like
e^x*e^y = e^(x+y) and
(e^x)^y = e^(x*y) and
(e^x)^(e^y) = e^(xe^y)
so for tetration we might expect
(where ^xe means e tetrated to x) (and * means multiplication)
^xe*^ye = ^(x*y)e
^y(^xe) = ^(x^y)e
^(^ye)(^xe) = ^(x^(^ye))e
translated:
e tetrated to x times y tetrated to e = (x times y) tetrated to e
(e tetrated to x) tetrated to y = e tetrated to (x to the y)
(e tetrated to x) tetrated to (e tetrated to y) = e tetrated to (x to the (e tetrated to y))
does this sound reasonable?