Here is question on an math assignment I was given, I have no clue what it is even asking.

It's a Challenge Yourself question, I've typed it exactly how it is on my paper:

A student is having difficult figuring out what is wrong with his proof:

Let C=D
C^2=CD
C^2 - D^2 = CD - D^2
(C - D)(C + D) = D(C - D)
C + D = D
However C=D
D + D = D
2D = D
2 = 1 ???

If C=D, C-D=0 and you cannot divide by zero.

Oh I get it now! Thanks

It seems like you have encountered a classic math paradox known as the "proof" that 2 equals 1. Don't worry; it's not actually correct. This paradox is designed to trick people by using a hidden error in the calculations. Let's go through it step by step to understand where the mistake occurs.

The incorrect proof starts with the assumption that C = D.

1. C^2 = CD: This step is correct since both C and D are assumed to be equal.

2. C^2 - D^2 = CD - D^2: In this step, the difference of squares formula is applied, correctly factoring the left side of the equation.

3. (C - D)(C + D) = D(C - D): Here, both sides of the equation are multiplied by (C - D). Still, at this point, the equation remains mathematically correct.

4. C + D = D: In this step, the error occurs. The problem arises when (C - D) is canceled out on both sides of the equation. Since C = D (from the initial assumption), subtracting D from both sides leaves us with C + D - D = 0 or C = 0.

When C is substituted with 0, the equation becomes 0 + D = D, which is true. However, this step is not valid because dividing both sides of an equation by (C - D) introduces division by zero, which is undefined.

Since the proof involves dividing by zero, which is not allowed in mathematics, the conclusion that 2 equals 1 is incorrect. Therefore, the error lies in the division step, making the proof invalid.

Remember that when you encounter situations that seem illogical or paradoxical, it is essential to carefully analyze each step in the solution for any mathematical errors or inconsistencies.