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#### find_the_fun

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- Feb 1, 2012

- 166

- Thread starter find_the_fun
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- Feb 1, 2012

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- Jan 26, 2012

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In the most general sense, it refers to the notion of "cardinality", "magnitude", "size", etc.. of the mathematical object in question. In this particular case, it denotes the number of edges in the edge set $E$.

A few possible meanings of the symbol (there are many more):

- For a set $S$, $|S|$ is the*number* of elements in $S$.

- For a complex number $x$, $|x|$ is the*distance* from $x$ to the origin.

- For a vector $\mathbf{v}$, $|\mathbf{v}|$ (sometimes denoted $||\mathbf{v}||$) is the magnitude or norm, that is, the*length*, of $\mathbf{v}$.

A few possible meanings of the symbol (there are many more):

- For a set $S$, $|S|$ is the

- For a complex number $x$, $|x|$ is the

- For a vector $\mathbf{v}$, $|\mathbf{v}|$ (sometimes denoted $||\mathbf{v}||$) is the magnitude or norm, that is, the

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- Oct 16, 2012

- 126

This will sound ridiculous but I have seen that mean "absolute value"?

\(\left|-3\right|=3\)

But I have hear that referred to as "magnitude" as well. I am just spitballing here; if I had to go with any one response, I would go with Bacterius.

EDIT: After re-reading Bacterius' post several times, mine almost looks childish...

\(\left|-3\right|=3\)

But I have hear that referred to as "magnitude" as well. I am just spitballing here; if I had to go with any one response, I would go with Bacterius.

EDIT: After re-reading Bacterius' post several times, mine almost looks childish...

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- Jan 17, 2013

- 1,667

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- Mar 5, 2012

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It's all the same thing.This will sound ridiculous but I have seen that mean "absolute value"?

\(\left|-3\right|=3\)

But I have hear that referred to as "magnitude" as well. I am just spitballing here; if I had to go with any one response, I would go with Bacterius.

EDIT: After re-reading Bacterius' post several times, mine almost looks childish...

The absolute value is the magnitude of the number, which is also the distance of the number -3 to the origin, or the length of the vector (-3) in 1 dimension.

In linear algebra $|| \cdot ||$ is often (but not always) used instead of $| \cdot |$ to distinguish the length of a vector from the magnitude of a scalar.

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- Mar 5, 2012

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That sort of seems to fit all categories, including sets.