ssncrockett
New member
- Joined
- Nov 2, 2011
- Messages
- 1
Here is the problem--The logic seems valid until you reach the end where 2=1????
Let’s start with two variables, x and y.
Let x = y (this is our starting equation).
Multiply both sides by x (OK because we don’t violate the equal sign – we’re ‘balancing’ our work across that sign). We get x² = xy.
Subtract y² from both sides (again OK because we don’t violate the equal sign).
We get x² – y² = xy – y².
Factor the left side. x² – y² = (x +y)(x – y).
Factor the right side. xy – y² = y(x – y).
Set these two factors equal to each other. They started that way, so there’s no problem here.
We get (x + y)(x – y) = y(x – y).
Now, since there's the same (x – y) factor on both sides of the equal sign, we can cancel them out..
We’re left with x + y = y.
But, we originally set x = y. Therefore, let’s replace x with y on the left side of the equation.
We get y + y = y. or 2y = y.
Now, the last step. We divide both sides by y. The result is 2 = 1!
OK, we know that if this proof is correct, then all of our math is entirely wrong.
After all, if 1 = 2, then 2 = 3, etc. But what’s the deal? Where did we go wrong?
That’s for you to figure out.
Let’s start with two variables, x and y.
Let x = y (this is our starting equation).
Multiply both sides by x (OK because we don’t violate the equal sign – we’re ‘balancing’ our work across that sign). We get x² = xy.
Subtract y² from both sides (again OK because we don’t violate the equal sign).
We get x² – y² = xy – y².
Factor the left side. x² – y² = (x +y)(x – y).
Factor the right side. xy – y² = y(x – y).
Set these two factors equal to each other. They started that way, so there’s no problem here.
We get (x + y)(x – y) = y(x – y).
Now, since there's the same (x – y) factor on both sides of the equal sign, we can cancel them out..
We’re left with x + y = y.
But, we originally set x = y. Therefore, let’s replace x with y on the left side of the equation.
We get y + y = y. or 2y = y.
Now, the last step. We divide both sides by y. The result is 2 = 1!
OK, we know that if this proof is correct, then all of our math is entirely wrong.
After all, if 1 = 2, then 2 = 3, etc. But what’s the deal? Where did we go wrong?
That’s for you to figure out.
