How can y + x = y - x?

How can y + x = y - x?

If y is 6, for example, and if x is 2.

That would be 6 + 2 = 6 - 2 or 8 = 4.

The most obvious answer is that it cannot be a valid equation.

Or if you subtract y from both sides you get x = -x

It is a valid equation, however, as you will now see.

The square root of 4 can be +2, or it can be -2,
because +2 times +2 = 4 and -2 times -2 = 4

We can replace x with the square root of 4 and get

y + sqrt(4) = y - sqrt(4)


Then we can make the equation like this:

y + (+2) = y - (-2) and that makes it
6 + 2 = 6 + 2 or 8 = 8

Or we can make the equation like this:

y + (-2) = y - (+2)
6 - 2 = 6 - 2 or 4 = 4

You can substitute any numbers for y and x and it will work the same way.

So, what does that say about the logic of mathematics?

It says that logic is circular and mathematics is quantum based.