# What does "arrow down" mean?

• May 16th 2011, 04:42 AM
julle
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.
• May 16th 2011, 05:49 AM
Plato
Quote:

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: $\displaystyle \lim _{x \to c^ + } f(x) = \lim _{x \downarrow c} f(x)$.
• May 16th 2011, 05:56 AM
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?
• May 16th 2011, 06:19 AM
Plato
Quote:

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.
• May 16th 2011, 11:55 PM
julle
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.