Silly Druid 6,904 November 15, 2023 Share November 15, 2023 What's wrong with this "proof" that 1 = -1? 1 1 Link to comment Share on other sites More sharing options...
Evil Pink One 13,506 November 16, 2023 Share November 16, 2023 14 hours ago, Silly Druid said: What's wrong with this "proof" that 1 = -1? Its the same proof for a troll to be an outstanding citizen!? Madness.... 1 Link to comment Share on other sites More sharing options...
Silly Druid 6,904 November 16, 2023 Author Share November 16, 2023 @StrawberryMilk Simp It is, because it's a well known fact that from any false statement you can derive any other false statement. Link to comment Share on other sites More sharing options...
Brony Number 42 10,069 November 21, 2023 Share November 21, 2023 The error is in taking the positive square root. sqrt(-1) = +/- i 2 This is my new signature. Link to comment Share on other sites More sharing options...
Silly Druid 6,904 November 21, 2023 Author Share November 21, 2023 @Thankful Brony 42 That's true, if you take one square root of -1 as +i and one as -i, then you get 1 in the end. This can be interpreted in multiple ways though, even the first step is questionable: while we usually only take the positive value of a square root into account, technically both 1 and -1 squared give 1, so the square root of 1 should be ±1. Dividing the square root of a product of two negative numbers into a product of their square roots can also cause this kind of problems. 2 1 Link to comment Share on other sites More sharing options...
SasQ 1,375 January 28 Share January 28 On 2023-11-21 at 4:15 AM, Brony Number 42 said: The error is in taking the positive square root. sqrt(-1) = +/- i I'd rather say that the error is in the silly notation that confuses the operation with its operands. But even the great Leonhard Euler fell into this trap, which shows that even the greatest minds can err if the notation they use is deceiving. The actual error is right there in the middle, because this is an identity only for real numbers. 1 My best posts list Recent post: Language Exchange Link to comment Share on other sites More sharing options...
Brony Number 42 10,069 January 28 Share January 28 It is like saying sin(0) = 0 = sin(pi) arcsin( sin(0) ) = 0 = arcsin( sin(pi) ) = pi 0 = pi You have period functions. If f(x) maps to A, and f(y) maps to A, it does not mean that x = y. When you take roots of numbers you should write them in polar notation R = r exp( t i) then R^(n) = r^(n) exp( t i / n) and there are multiple roots. Basically you dive the unit circle into 1 / n pieces. It's really interesting. This is my new signature. Link to comment Share on other sites More sharing options...
ForEverfreePegasis 25 August 29 Share August 29 On 2023-11-21 at 11:45 AM, Silly Druid said: @Thankful Brony 42 That's true, if you take one square root of -1 as +i and one as -i, then you get 1 in the end. This can be interpreted in multiple ways though, even the first step is questionable: while we usually only take the positive value of a square root into account, technically both 1 and -1 squared give 1, so the square root of 1 should be ±1. Dividing the square root of a product of two negative numbers into a product of their square roots can also cause this kind of problems. Wow. I never even thought about whether i would be negative or positive because it's an imaginary number I assumed that it wasn't positive or negative 1 Link to comment Share on other sites More sharing options...
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