1 + 1 = 0?

Let's investigate these equations:

1 + 1:
= 1 + sqrt (1)
= 1 + sqrt [(-1)(-1)]
= 1 + sqrt (-1) x sqrt (-1)
= 1 + i x i
= 1 + (-1)
= 1 - 1
= 0

From this demonstration, it would appear that 1+1=0.
Right?
Right!

...right?

Well, we know it's wrong. Let's find the mistake. 1+1 obviously equals 1 + sqrt (1), so no problem yet. The next is also correct, seeing as (-1)(-1) equals 1. Here is the mistake, however:

When imgaining what sqrt(-1) could be, we come to the conclusion of terming it 'i' (for imaginary) in replacement of a better term or solution. Therefore, 1 + sqrt[(-1)(-1)] DOES NOT facilitate i^2 because no longer do we use the variable i since the expression can be SIMPLIFIED. Instead, we simplify (-1)(-1) and get 1, not i^2. Becuase simplifying the expression (-1)(-1) yields the product of 1 instead of -1, we continue to solve 1 + 1 = 1 + 1, getting the result: 2 = 2, the solution. Problem solved.

The mistake lies here:

= 1 + sqrt (-1) x sqrt (-1)

We don't need to separate the sqrt because the parenthases can be solved first (as provided by the order of operations.)

Did you understand why it is wrong? Hope you did! Post your thoughts in a comment.

P.S. do you want me to do more maths posts like this one? I could do one about 2+2=5...

LOL

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