'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?
Hello, the kopite!
$\displaystyle \begin{array}{c}\dfrac{x}{x}-1\:=\:0 \\ \\[-4mm] x\:=\:0 \end{array}$
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 $\displaystyle \frac{x}{x}-1 \:=\:0$, then: .$\displaystyle \frac{x}{x} \:=\:1$ . . . which is true if $\displaystyle x \neq 0$
If $\displaystyle x = 0$, the other statement is not true because $\displaystyle \frac{0}{0}$ is indeterminate.