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wu :: forums    riddles    general problem-solving / chatting / whatever (Moderators: Grimbal, towr, Icarus, Eigenray, ThudnBlunder, SMQ, william wu)    An Exponential Curiosity « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: An Exponential Curiosity  (Read 413 times) Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 An Exponential Curiosity   exponential_graph.gif « on: Jan 29th, 2005, 10:19am » Quote Modify Clearly x2/6 = x1/3, or does it?   As x2/6 = (x1/6)2 = (x2)1/6...   (-1)1/3 = -1, (1[pm][smiley=i.gif][surd]3)/2 [three values] ((-1)1/6)2 = -1, (1[pm][smiley=i.gif][surd]3)/2   However, ((-1)2)1/6 = -1, (1[pm][smiley=i.gif][surd]3)/2, but also 1, -(1[pm][smiley=i.gif][surd]3)/2 [six values]   Consider the two graphs below: (i) y = x1/3, (ii) y = (x2)1/6.   Spot the difference?         [e]Thanks for the correction, rmsgrey.[/e] « Last Edit: Jan 29th, 2005, 3:11pm by Sir Col » IP Logged mathschallenge.net / projecteuler.net rmsgrey Uberpuzzler     Gender: Posts: 2874 Re: An Exponential Curiosity   « Reply #1 on: Jan 29th, 2005, 2:12pm » Quote Modify on Jan 29th, 2005, 10:19am, Sir Col wrote: ((-1)1/6)2 (has six complex values) I get [pm]i6=-1 and that: ((-1)1/6)2=-1 (and 2 complex values)=(-1)1/3 IP Logged Icarus wu::riddles Moderator Uberpuzzler Boldly going where even angels fear to tread.     Gender: Posts: 4863 Re: An Exponential Curiosity   « Reply #2 on: Jan 29th, 2005, 9:02pm » Quote Modify Impudent monkey indeed. You know very well that exponentiation cannot be extended to domains completely encircling 0 in the complex plane. Yet that is exactly what you attempt here! IP Logged "Pi goes on and on and on ... And e is just as cursed. I wonder: Which is larger When their digits are reversed? " - Anonymous Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: An Exponential Curiosity   « Reply #3 on: Jan 30th, 2005, 2:15am » Quote Modify Cheeky by name, cheeky by nature...   But what about the real graphs?   Why is the graph of y = (x2)1/6 different to y = x1/3, when (x2)1/6 = x2/6 = x1/3?   Does that mean that 2/6 is not equal to 1/3? IP Logged mathschallenge.net / projecteuler.net Barukh Uberpuzzler     Gender: Posts: 2276 Re: An Exponential Curiosity   « Reply #4 on: Jan 30th, 2005, 6:26am » Quote Modify on Jan 30th, 2005, 2:15am, Sir Col wrote: But what about the real graphs?   Why is the graph of y = (x2)1/6 different to y = x1/3, when (x2)1/6 = x2/6 = x1/3?   Does that mean that 2/6 is not equal to 1/3? Why complicate the question? Consider two functions: (i) y = x; (ii) y = [sqrt](x2) IP Logged Icarus wu::riddles Moderator Uberpuzzler Boldly going where even angels fear to tread.     Gender: Posts: 4863 Re: An Exponential Curiosity   « Reply #5 on: Jan 30th, 2005, 11:24am » Quote Modify More to the point, that (xa)b = xab rule comes with an "x [ge] 0" qualifier. « Last Edit: Jan 31st, 2005, 4:11pm by Icarus » IP Logged "Pi goes on and on and on ... And e is just as cursed. I wonder: Which is larger When their digits are reversed? " - Anonymous Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ => general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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