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| "Jim Kelley" | wrote in message ... | | [...] | | "X-rays will prove to be a hoax." | | http://zapatopi.net/kelvin/quotes/ | | ac6xg | ---------------------------------------------------------- A I hope you will excuse me the next example. Let f = Sin[x] I choose: x = 2*k*pi and k goes to infinity one by one: 0, 1, 2, ... Definitely then I found correctly f(oo) = 0. Cecil chooses: x = 2*k*pi + pi/2 and k goes to infinity one by one, as before. Definitely he founds correctly f(oo) = +1 Lord Kelvin chose: x = 2*k*pi - pi/2 and k went to infinity one by one, as above. Definitely he founded correctly f(oo) = -1 All of us we are correct in all steps, but the value f(oo) does not exist as a single one. In fact f(oo) takes every value between -1 and +1. f(oo) definitely depends on the way in which each one of us went to infinity. IMHO: this is the kind of behavior of Zinp. B But in addition to that there is one more to say: Zinp is a result of the order in which we consider the limits for the wire radius and the length to wavelength ratio. If a is the wire radius and L/wl is the ratio of length to wavelength then I can imagine five cases: 1 First the a is going to zero, a formula is produced for Zinp, then the L/wl is going to infinity and a number may or may not be the result for Zinp. 2 First the L/wl is going to infinity a formula is produced for Zinp, then the a is going to zero and a number may or may not be the result for Zinp. 3 Simultaneously, both the L/wl is going to infinity and the a is going to zero, and a number may or may not be the result for Zinp. 4 We keep a constant value for L/wl, then a is going to zero and a number may or may not be the result for Zinp. 5 We keep a constant value for a, then L/wl is going to infinity and a number may or may not be the result for Zinp. [ On the occasion I have to confess that the movie at [ http://antennas.ee.duth.gr/ftp/visua...s/fu010100.zip [ 850 KB [ belongs to the last case. For a possible conclusion let me mention a remarkable note from a Mathematical book: "The biggest source of erroneous conclusions have to do with the order we consider the limits" (and which order we tend then to forget ... ) Sincerely, pezSV7BAXdag |
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