1 = -1 :A Mathematics Paradox #shorts

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☝️Can you spot the error in this mathematical reasoning? #shorts

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#Paradox #Shorts #Mathematics
  1. Pen and Paper Science
  2. Mathematics Paradox
  3. Paradox
  4. -1 = 1
  5. 1 = -1
  6. Pen and paper science
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Комментарии
Автор

We need to keep in mind that:

√a * √b = √(ab)
√-a * √b = √(ab) * i
√a * √-b = √(ab) * i
√-a * √-b = - √(ab)

Nice short video though!

icebeartwo
Автор

No, the REAL square root of 1 is always 1 ( only one value ("solution" ), but x^2 = 1 has the two solutions x = +/- sqrt(1) = +/-1.


The COMPLEX squareroot function ( sqrtc) has however several values ( a multi-valued function with multiple branches ).

So sqrtc(1) = 1 & -1 (main values)
= e^(ipPI), where p is an integer.

Or
1 = 1, Theta = 0, +/- 2PI, +/- 4PI, +/- 6PI ... &
- 1 = 1, Theta = +/- PI, +/- 3PI, +/- 5PI ...

Bjowolf
Автор

Either define √x as +√x OR -√x
Or √x is undefined for negative and complex input

lillii
Автор

1 is equal to -1, just that -1 is moving in the opposite direction

MrRichie