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The Meaning of || in Math — Explained in Great Detail

The Meaning of || in Math — Explained in Great Detail

For those among us who are not particularly mathematically inclined, it can be difficult to remember the meanings of mathematical symbols.

This can be the case regardless of whether we learned them twenty years ago or yesterday. 

The symbols for addition, subtraction, division, and multiplication are pretty straightforward.

Things become more complicated, however, when we begin to talk about the branch of mathematics known as geometry, not to mention trigonometry or calculus.

But take courage! Fortune favors the brave, and you are never too old to relearn the basic meanings of different mathematical concepts. 

Have you come across the symbol || in a text and are unsure what it signifies? No problem. Here is a quick cheat sheet to this symbol’s two meanings. 

 

What does || mean in math?

The symbol || has two meanings. The first meaning indicates parallelism in geometry. If AB and CD are both lines on a common plane, then “AB || CD” means they are parallel. Its second use is to denote a norm when used as brackets. The norm value in between two brackets is the length of a vector.

 

Parallelism in Geometry

Geometry is a branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues. 

More simply, it is a way to study the sizes, shapes, positions, angles, and dimensions of things. 

When most of us think about geometry, we picture a series of circles, squares, and triangles. We may also recall a variety of different formulas we were taught that helped us figure out the lengths and surface areas of those shapes. 

Another thing we may remember, is learning about parallel lines. Parallel lines are lines in a plane that do not meet.

If two lines exist on the same plane without every intersecting at any point, then they are parallel. 

Curves that don’t intersect may also be considered parallel. 

In three-dimensional Euclidean geometrical spaces, two planes or a line and a plane that do not share points are also parallel. 

Two lines that do not meet in three-dimensional space must be on the same plane in order to be parallel. If they are not, they are called skew lines. 

Last but not least, planes themselves can also be parallel. Parallel planes are planes in the same three-dimensional space that never intersect. 

The symbol for parallelism is ||. 

To signify that two lines are parallel, you can place the names of the lines on either side of this symbol. For example, AB || CD means that the line AB runs parallel to the line CD.

 

Norms

The norm of a mathematical object is a quantity that describes the length, size, or extent of that object. 

The double bar symbol is reserved for vector norms. It is used in pairs on either side of the value of the vector norm, for example || X ||.

Vector norms specify the length of a vector. A vector is a mathematical object that looks like an arrow.

It has a length, known as the magnitude or norm, and a direction. 

In two dimensions, you can find the vector norm using the Pythagorean theorem.

The Pythagorean theorem provides that the sum of the squares on the legs of a right triangle is equal to the hypotenuse, and is normally written as: a2+b2=c2.

In three dimensions, the Pythagorean theorem simply gets another letter: a2+b2+c2=d2