With sheet music, what happens with sharps and double sharps that are already sharped in the key signature?

1. Do double sharps carry through the measure?
2. Can double sharps be found in a key signature?
3. Why do composers use double sharps?

Do double sharps carry through the measure?

The double sharp symbol alters the pitch of the note to which it is attached as well as any subsequent occurrence of the same note (identical line or space) in the same measure. ... Any note with a double sharp that also has a tie across a barline carries the double sharp to the note on the other side of the barline.

Can double sharps be found in a key signature?

Double-flats and double-sharps are often used as accidentals, but placing them in the key signature (in music that uses equal temperament) makes the music generally impractical to read.
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The need to consider theoretical keys.

Why do composers use double sharps?

The purpose of double sharps and flats in key signatures is to represent this scale in the way it is written, and avoid constant use of accidentals on a note - as per the example switching between G and G#.