# What does the notation | | mean?

#### find_the_fun

##### Active member
For example my text book reads if G(V, E) is a pseudograph then $$\displaystyle \sum\limits_{v \in V} deg(v) = 2|E|$$

#### Bacterius

##### Well-known member
MHB Math Helper
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 $\mathbf{v}$.

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#### alane1994

##### Active member
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...

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#### ZaidAlyafey

##### Well-known member
MHB Math Helper
As far as I know for a graph $G$ , $V$ represent vertices and $E$ represent Edges . A distance in a graph does not make sense , so $$\displaystyle |E|$$ would be the number of edges .

#### Klaas van Aarsen

##### MHB Seeker
Staff member
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...
It's all the same thing.
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.

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Actually, I like to call it the "size" of whatever you use it for.
That sort of seems to fit all categories, including sets.