What is the difference between single and double modulus signs. Do they both mean magnitude?

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What's the difference between a set of single modulus and a set of double modulus signs?

On textbooks I have seen the magnitude of two vectors vector as $|\mathbf{x} - \mathbf{y}|$ but I've seen other sites where they've presented it as $\|\mathbf{x} - \mathbf{y}\|$. Also, for derivatives does $|c'(x)| = \|c'(x)\|$?

Thanks.

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It depends on what notation the author has decided to use, but $| \cdot |$ is usually reserved for the absolute value of a real number, or the modulus of a complex number, whereas $\| \cdot\|$ is reserved for the norm of a vector.