About 0^0 > Even for discrete things like elements of GF(5)? I haven't thought > about what 0^0 is for things where the continuous limit doesn't make sense. > In any ring, integer power x^n is défined by x^0 = 1, because an empty product is the unit element. The reason is the same for 0!=1. But x^(-n) is only defined if x has an inverse.
In analysis 0^0 is undefined because it's a undefined limit: un^vn = exp(un * log vn). Try with un=1/n et vn=1/n and limit un^vn == 1 But for un=a/log n -> 0 and vn=1/n -> 0 un*log vn =-a and un^vn -> e^(-a) != 1. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
