Briefly

1 + 1 = 3

1 + 1 = 3

It may sound somewhat paradoxical, but we are going to crumble the foundations of mathematics by demonstrating that 1 + 1 is equal to 3.

We begin with an unquestionable equality:

We add both members of equality the same amount:

We can transform the previous expression into:

If we look, we see that we have on both sides the result of squareing a binomial, so we can simplify:

If we extract the square root of both members we have that:

Or what is the same

That is:

How is it possible?

Solution

The error is that of the expression:

It was deduced that

Although the squares are the same, the first powers are not identical, for example:
but -5 is not equal to 5.