1. ## [SOLVED] Notation

What does $\displaystyle \frac{| \tilde x^{(0)} - x^{(0)} | } {max \lbrace 1, | x^{(0)} | \rbrace} \ge \epsilon$ mean, particularly the comma in the denominator? And do the brackets have any special meaning wrt the $\displaystyle x^{(0)}$?

2. Originally Posted by garymarkhov
What does $\displaystyle \frac{| \tilde x^{(0)} - x^{(0)} | } {max \lbrace 1, | x^{(0)} | \rbrace} \ge \epsilon$ mean, particularly the comma in the denominator? And do the brackets have any special meaning wrt the $\displaystyle x^{(0)}$?
$\displaystyle \max\{a,b\}$ means the larger of the numbers a and b.

3. Originally Posted by Opalg
$\displaystyle \max\{a,b\}$ means the larger of the numbers a and b.
Thanks. And do you know if $\displaystyle x^{(0)}$ has any special meaning distinct from $\displaystyle x^{0}$ ?

4. Originally Posted by garymarkhov
Thanks. And do you know if $\displaystyle x^{(0)}$ has any special meaning distinct from $\displaystyle x^{0}$ ?
That would depend on the context. As far as I know, there is no standard meaning for superscripts in parentheses, as in $\displaystyle x^{(0)}$.

5. Originally Posted by garymarkhov
Thanks. And do you know if $\displaystyle x^{(0)}$ has any special meaning distinct from $\displaystyle x^{0}$ ?
As a side note: in general convention, if you see $\displaystyle x^{(n)}$ where $\displaystyle n \ge 4$, it represents the nth derivative of x.

6. Originally Posted by mathemagister
As a side note: in general convention, if you see $\displaystyle x^{(n)}$ where $\displaystyle n \ge 4$, it represents the nth derivative of x.
Interesting, thanks.

7. It is also often used for sequences.

That is $\displaystyle x^{(0)}$ would be the first term of some sequence $\displaystyle (x^{(k)})_{k\in\mathbb{N}}$.