False Proof is one of the concepts in Mathematics...
Can you prove 1 = -1?
Version 1:
Amazing. Isn’t? This is called False Proof.
There is one more way to prove 1 = -1.
Version 2 :
Now let us see, how is this possible?
Let us take the first proof (False Proof)
The rule is
generally valid only if at least one of the two numbers x or y is positive, which is not the case here. Alternatively, one can view the square root as a 2-valued function over the complex numbers; in this case both sides of the above equation evaluate to {1, -1}.
How about the second version? Is that true? The answer is false again. Below is the explanation.
The equation a bc = (a b )c, when b and/or c are fractions, is generally valid only when a is positive, which is not the case here, leading to an invalid proof.
Can you prove 1 = -1?
Version 1:
There is one more way to prove 1 = -1.
Version 2 :
Let us take the first proof (False Proof)
The rule is
generally valid only if at least one of the two numbers x or y is positive, which is not the case here. Alternatively, one can view the square root as a 2-valued function over the complex numbers; in this case both sides of the above equation evaluate to {1, -1}.How about the second version? Is that true? The answer is false again. Below is the explanation.
The equation a bc = (a b )c, when b and/or c are fractions, is generally valid only when a is positive, which is not the case here, leading to an invalid proof.
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