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 Skip Navigation LinksMath Help > Math Jokes > Proof that 1 = -1

Here is the famous proof that tumbles the very foundations of mathematics:

Proof that 1 = -1.

-1  =  -1
Assert that -1 = -1.
 1    =   -1 
-1  1
Express -1 in two different, but equivalent ways.
  =  
  1   -1 
 -1   1
Take the square root of both sides
  =  
  1   -1 
  -1   1 
Use the fact that    =  
  x    x 
  y  
 y 
 1    =    i 
 i  1
Simplify all the square roots.  Note that the square root of -1 is defined as i.
  i     =    i²
  i  1
Multiply both sides by i.
1   =    -1 
  1
i/i is 1, and i² is -1.
1  =  -1
Proof is complete!
 

Related pages in this website

Index of joke proofs


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