Here is an example of the double sharp (within the red mark) from Liszt Les Preludes, see below.
I suppose this notation "x" is called double sharp.
What are (1) the definition, and (2) the origin of this notation x?
This is a common notation in the violin sheet music. Does this notation occur often in other instruments, too?
I suppose to raise a semitone higher than the designed sharp ♯ tone. But I would like to know a precise definition, because within the bar, other than the chosen key, there could be other preceding notations sharp (♯ or #), the flat (♭ or b), or the natural sign ♮.