# Thread: simple implication problem

1. ## simple implication problem

'x/x-1=0'
'x=0'
what is the link between these two statements?
i would say that its obvious that the link is 'if and only if'!
but i'm wrong. can someone please help?

2. Originally Posted by the kopite
'x/x-1=0'
'x=0'
what is the link between these two statements?
i would say that its obvious that the link is 'if and only if'!
but i'm wrong. can someone please help?
Well clearly, $\frac{x}{x-1} = 0 \Leftarrow x=0$
Only if $x \neq 1$, the expression $\frac{x}{x-1}$ is defined and $\frac{x}{x-1} = 0 \Rightarrow x=0$

3. Hello, the kopite!

$\begin{array}{c}\dfrac{x}{x}-1\:=\:0 \\ \\[-4mm] x\:=\:0 \end{array}$

What is the link between these two statements?

Not sure how to describe a "link" . . .

The two statements are mutually exclusive.
. . Only one of them can be true.

If $\frac{x}{x}-1 \:=\:0$, then: . $\frac{x}{x} \:=\:1$ . . . which is true if $x \neq 0$

If $x = 0$, the other statement is not true because $\frac{0}{0}$ is indeterminate.

4. soroban got my question wrong, sorry if i didnt explain my equation properly. but i didnt understand the second part of ismorphism's explanation. i'm slow on genral reasoning.

5. Originally Posted by the kopite
'x/x-1=0'
'x=0'
what is the link between these two statements?
i would say that its obvious that the link is 'if and only if'!
but i'm wrong. can someone please help?
I agree that it is 'if and only if'.

If $x=0$ then $\frac{x}{x-1}=0$. If $\frac{x}{x-1}=0$ then $x=0$.

Both of those are true statements.