## Puzzler

This a puzzle for me.

x^3 -x -x^3=0 Obviously x=0
but, divide both sides by x

x^2 -1 -x^2=0 except for when x=0 'cause undefined
but that means
-1=0

is this apparent conflict not in fact one because you can't rule out x=0 ?
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 [QUOTE=regor60]This a puzzle for me. x^2 -1 -x^2=0 except for when x=0 'cause undefined but that means -1=0 QUOTE] Hmm looks to me like you would have -1 = 0/x But x = 0 so you have -1 = 0/0 0/0 is undefined. -1 = undefined is not well formed equation. Any know better mathematical terminology for 0/0?
 $$x^3 - x - x^3 = 0$$ then divide by x: $$\frac{x^3 - x - x^3}{x} = \frac{0}{x}$$ $$x^2 - x^2 = 1$$ Even saying that $$\frac{0}{x}$$ is 0 you should see that it is not possible to get two different numbers to make 1 when the two x values will give the same to take away. The Bob (2004 ©)

## Puzzler

I thought that -1=0 is not a statement of equality, but more of a qualifier for the original equation. We want to know when say, x^2 - x^2 == 1, and that will only happen when 0 = 1, which is never. So that has no solution. I thought this meaning was always implied in mathematics. I mean I can say
1 + 1 =5, but how can that be?! I mean I just wrote it, but its not supposed to be possible! Just becasue yo ucan write down an equation doesnt mean its true.

 Quote by regor60 This a puzzle for me. x^3 -x -x^3=0 Obviously x=0 but, divide both sides by x x^2 -1 -x^2=0 except for when x=0 'cause undefined but that means -1=0 is this apparent conflict not in fact one because you can't rule out x=0 ?
You are simply breaking the rule of "not dividing by zero".
You could state your "problem" simpler:
x = 0
divide both sides by x
x/x = 0/x <-> 1 = 0

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