# There are some walls in my Math formula. |a|

## What's the meaning of variables surrounded by two vertical lines?

In this post i'm trying to shed some light on the cryptic nature of mathematic formulas. This is definition is guaranteed to be incomplete because i don't know shite about math. 💩

What does it mean if a variable in a Mathematics formula is surrounded by two vertical lines?

According to WolframAlpha "`|z|` is the absolute value of z." I guess whether I take `|z|` or `|a|` doesn't really matter, so I'll continue with `|a|` as it seems more common.

In laymen terms this the statement from WolframAlpha means we're taking the actual value from `a` while disregarding the algebraic sign (`+` or `-`).

So if `a = -2.5` then `|a|` represents the value `2.5`

If `a = 3.14` then `|a|` equals the value `3.14`

You can see the two `|` `|` surrounding the variable name as some kind of programming function that returns the distance from `0` to `a`. In-fact it exists in languages like `C#` as the `{Math.Abs(value)}` function. But even if this function wouldn't exist in your programming language of choice you could implement it as `sqrt(a^2)` (sqrt is the square-root). Making `a` squared gets rid of the algebraic sign (22 and -2-2 are both 4). And the square root reverses the effect of the quadration without gaining back the algebraic sign.

In mathematical terms `|a|` you may come across this notation described ast the `absolute value` or `modulus` of the real number `a`.

In case you're looking for a more exhaustive definition, I can recommend this 3 part video by Eddie Woo.