# Thread: What does "arrow down" mean?

1. ## What does "arrow down" mean? [SOLVED]

Hi all.

I need some help to understand this, what should be simple, sentence:

Since a \to b as c \downarrow 0 it was shown that...

What does the down arrow mean? It can not mean "goes to", since c is a constant. I'm thinking it is meaning something like "c is a small positive number" ??

Thanks.

2. Originally Posted by julle
Since a \to b as c \downarrow 0 it was shown that...[/I]
What does the down arrow mean? It can not mean "goes to", since c is a constant. I'm thinking it is meaning something like "c is a small positive number" ??
That is limit from the right, from above: $\displaystyle \lim _{x \to c^ + } f(x) = \lim _{x \downarrow c} f(x)$.

3. Thanks for reply. Not sure I understand, though.

If it is the same, why should the author use two different arrows in the same expression?

4. Originally Posted by julle
Thanks for reply. Not sure I understand, though. If it is the same, why should the author use two different arrows in the same expression?
They are not the same, I did not say they were.

$\displaystyle a \to b$ as $\displaystyle c \downarrow 0$ is read "a approaches b as c approaches 0 from the right."

Some authors use $\displaystyle \lim _{x \to c^ + }$ (note is + in the exponent on c).
While others use $\displaystyle \lim _{x \downarrow c}$.
Now those have the same meaning.

5. Okay, thanks.

One last thing: What does "from the right" mean? Does "from the right" equal the positive numbers, and "from the left" equals negative numbers?

Edit:
That makes sense, since c never is negative.

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