What math symbol would I use for never equal to

[richyw]

What math symbol would I use for "never equal to"

alright so I know that $$1\neq 2$$ means that "1 is not equal to 2" right?

so could I say that $$e^x\neq 0$$. Would this mean that e^x is never equal to 0? I know it seems small, but it confuses me a bit.

also what would I say if I had a function of another function, where the first function is not true if the second function is equal to some value, if that makes any sense.

Like if I said $$f(g(x))\neq 0 , g(x)=k$$ would that be saying that f(g(x) is not equal to zero as long as g(x) is equal to some number?

I've tried searching this and am just really confused. I have to start learning this stuff because my homework is slowly getting filled with all of these upside down v's and backwards E and stuff!

 

[Robert1986]

That seems right for the first one. For the second one try:
$g(x) = k \Rightarrow f(g(x)) \neq 0$ or $f(g(x)) \neq 0$ whenever $g(x) = k$.

 

[Mark44]

For the first one, you could use a qualifier, "for all."

$\forall x \in \mathbb{R}, e^x > 0$

The upside-down A means "for any," "for all," or "for each." I wrote e^x > 0 rather than e^x ≠ 0 to be more specific.

 

[richyw]

thanks a lot!