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!

 

[CellCoree]

I would recommend using the "not equal to" symbol, which is ≠. This symbol means that two quantities are not equal to each other. So in the first example, e^x ≠ 0 means that e^x is never equal to 0.

In the second example, f(g(x)) ≠ 0, g(x) = k, means that the function f is not equal to 0 when g(x) is equal to some value k. Essentially, g(x) = k is a condition or criteria for when the function f is not equal to 0.

I understand that mathematical symbols can be confusing and overwhelming, but with practice and guidance, they become easier to understand. Keep learning and don't be afraid to ask for help when needed.