# Thread: Not defined problem

1. ## Not defined problem

My last maths question today is this....

"Explain what is wrong with this argument"

$x(x+1)=0$ is equivalent to $x(x+1)/(x+1)$(divided both sides by (x+1)

So the solution to $x(x+1)=0$ is $x=0$

2. Originally Posted by wolfhound
My last maths question today is this....

"Explain what is wrong with this argument"

$x(x+1)=0$ is equivalent to $x(x+1)/(x+1)$(divided both sides by (x+1)

So the solution to $x(x+1)=0$ is $x=0$
if x(x+1) = 0 , then x = 0 or (x+1) = 0, making x = -1 another solution.

division by 0 in the form of (x+1) ist verboten!

3. Ok thanks , so for both solutions the equation is undefined because if I use the value of x=-1 I will be dividing by zero which is forbidden?(same with x=0 forbidden)

4. Ok thanks , so for both solutions the equation is undefined because if I use the value of x=-1 I will be dividing by zero which is forbidden?(same with x=0 forbidden)
Which equation? There is nothing undefined about x(x + 1) = 0. On the other hand, dividing both sides by x + 1 is in fact a statement that says,

For all x, x(x + 1) = 0 iff x(x + 1)/(x + 1) = 0

This statement is false for x = -1.

That is why, when simplifying an equation, it is important to write not just a sequence of equations E1 = E'1, E2 = E'2, ..., but also the logical relationship between the them, e.g., E1 = E'1 <=> E2 = E'2 => E3 = E'3, ... In the example above,

x(x + 1) = 0 <= x(x + 1)/(x + 1) = 0

is OK, but

x(x + 1) = 0 <=> x(x + 1)/(x + 1) = 0

is not.

5. Ok thanks,
but what does this arrow mean? x(x + 1) = 0 <= x(x + 1)/(x + 1) = 0

6. It's just my notation for "is implied by", or "if", or "follows from" whereas <=> means "if and only if".