# What the star means next to x?

1. Jun 6, 2005

### amcavoy

I was just wondering what the star means next to x? For example:

$$f(x^{*})$$

Thanks.

2. Jun 6, 2005

### Icebreaker

In what context? In Riemann sums, they denote some particular partition, although that's more often paired with a subscript.

3. Jun 7, 2005

### matt grime

* could mean complex conjugate, and is most likely. Unlikely is that it is some form of duality statement.

4. Jun 7, 2005

### arildno

It might also mean that given a function f(x), we signify (for example) the ROOTS of f with $$x^{*}$$
Each root of f fulfills the equation:
$$f(x^{*})=0$$
(In this case, therefore, $$x^{*}$$ is used as a symbol for an element of that subset R of the domain D of f which consists of the roots of f. The star distinguishes these x-values then from the rest of the x-values in D but not included in R.)

It is impossible to determine what is meant here without giving us the proper context.

EDIT:
Note that attachment of a star is a STANDARD notation for the complex conjugate (i.e, Matt Grime's suggestion); several authors don't bother to introduce a star symbol to denote specific roots (or elements of other subsets of the domain). However, some do, although it cannot be regarded as a standard or normative notation.

Last edited: Jun 7, 2005