Triple bar (equal sign)

[Lovisa W]

In the video ‘Notation: functions’ you use a triple bar (equal sign with three lines). Could you please clarify what that sign means, especially in the context of functions, (e.g., for the magnitude function, like |3|)?
Thanks.

[Simon]

That symbol means “is equal by definition“. We use it when we want to make it clear that the right-hand side of the equation means the same thing as the left-hand side. In other words, no derivation or manipulation or intermediate steps are needed to derive the right-hand side from the left-hand side.

It would be fine to use the normal equals sign (=) in this situation too, but the “equal by definition” is meant to be more helpful to the reader.

[Author]

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