Dear all,
Regarding operation on inf.. is it true that..
0^0 = 1^inf = inf^0 .. ?
because..
1^inf
= lim(x -> inf) 1^x
= lim(x -> inf) ((1/x)^0)^x
= lim(x -> inf) (1/x)^0
= 0^0
and similarly..
1^inf
= lim(x -> inf) 1^x
= lim(x -> inf) (x^0)^x
= lim(x -> inf) x^0
= inf^0
Therefore if we define 0^0 = 1 then we should also define 1^inf = 1
and inf^0 = 1.
Otherwise if we define 0^0 = undef then we should define 1^inf and
inf^0 to be undef.
It looks like that Maple defines
0^0 = 1^inf = inf^0 = 1
and Mathematica defines
0^0 = 1^inf = inf^0 = undef
Best regards,
bowo