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 Nir Dahan Inner circle Munich, Germany 1390 Posts Posted: Jun 27, 2005 06:22 pm    0 Since there were a few of those posted lately I thought why not post another - sorry if it was already posted... -1 = -1 -1/1 = 1/-1 sqrt(-1/1) = sqrt(1/-1) sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1) multiply in diagonals... sqrt(-1) * sqrt (-1) = sqrt(1) * sqrt(1) cancel the sqrt... -1 = 1 !!!!!! has the world of numbers gone bizzare ????!!! or could you help "captain math" find the error ??? Adventures in ASIC digital design stanalger Special user St. Louis, MO 996 Posts Posted: Jun 27, 2005 06:47 pm    0 Error occurs when going from line 3 to line 4. sqrt(a/b) = (sqrt(a)) / (sqrt(b)) only if all of the square roots are real numbers. James F Inner circle Atlanta 1097 Posts Posted: Jun 27, 2005 07:08 pm    0 http://www.themagiccafe.com/forums/viewt......01&2 that's close to what I posted. At least the errors in the math is the same. That mistake is pretty tough to catch if you aren't up on your math. James Nir Dahan Inner circle Munich, Germany 1390 Posts Posted: Jun 28, 2005 01:32 am    0 Stan, we don't assume real numbers only. complex numbers are allowed and the mistake is not there... it is somewhere else. there is a more beautiful version of this "falacy" in the Moscow puzzles book. look for the mosquito and elephant puzzle. the one in the book is even more hard to catch. Nir Adventures in ASIC digital design TomasB Inner circle Sweden 1143 Posts Posted: Jun 28, 2005 01:47 am    0 I guess it is from going to line 3 as you have missed writing all solutions when you take the root out of both sides of the equation. The solution you decided to keep is not the correct one. /Tomas Nir Dahan Inner circle Munich, Germany 1390 Posts Posted: Jun 28, 2005 02:50 am    0 Right Tomas! if you have the moscow puzzles book try to look up the similar problem there. that is by far more hidden in their problem... Adventures in ASIC digital design Jonathan Townsend Eternal Order Ossining, NY 27019 Posts Posted: Jun 28, 2005 08:01 am    0 I got lost when you suggested that i/1 == 1/i ie I = (i)**-1 ...to all the coins I've dropped here stanalger Special user St. Louis, MO 996 Posts Posted: Jun 28, 2005 08:45 am    0 Jonathan, Agreed. There is no error on line 3. The error certainly occurs when you go to line 4. Earlier I wrote: sqrt(a/b) = (sqrt(a)) / (sqrt(b)) only if all of the square roots are real numbers. I shouldn't have included the word "only". Perhaps I should have said: sqrt(a/b) = (sqrt(a))/(sqrt(b)) whenever a is a non-negative real number and b is a positive real number. Although it is also true in some other cases, it is not true for all real a, b. Case in point: sqrt(1/-1) is not equal to sqrt(1) / sqrt(-1). (But sqrt(-1/1) is equal to sqrt(-1) / sqrt(1).) Stan Jonathan Townsend Eternal Order Ossining, NY 27019 Posts Posted: Jun 28, 2005 10:11 am    0 There are usually two square roots of a number. We call one of them the principal root. ...to all the coins I've dropped here James F Inner circle Atlanta 1097 Posts Posted: Jun 28, 2005 10:45 am    0 A lot of people say the fallacy comes by not writting the "plus or minus" sign. (as stated by Nir Dahan) However, with this example the fallacy is simplifying sqrt(-1/1) = sqrt(1/-1) as sqrt-1/sqrt1 = sqrt1/sqrt-1 ...You cannot do that. Although in a lot of cases this will work it will not work all the time and it is the source of fallacy so strangler was correct. Read his explanation, it is right on. James The Magic Cafe Forum Index » » Puzzle me this... » » -1 = 1 (0 Likes)
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