Notes that are shorter in duration than quarter notes have flags on their stems what is the purpose of the flags

The purpose of having flags on the stems of the notes is, this indicates that for each flag, the note's value is cut smaller by half. The more flags a note has, the shorter its length is. This has also the same purpose with beams. Notes smaller than quarter notes have flags or beams. Hope this answer helps.

Idon’t think it’s true but if it is then you should make up a case then prove it