# Difference between revisions of "The order of terms matters even when they commute"

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[[Category:Inconsistencies]] | [[Category:Inconsistencies]] | ||

[[Category:Unspoken conventions]] | |||

When writing | When writing an expression that consists of several terms, the conventions regarding their order appear arbitrary. | ||

==Multiplication== | |||

It is usual to write: | |||

* \(xy\) and \(yx\) in either order; | * \(xy\) and \(yx\) in either order; | ||

* \(5t\) but not \(t5\) (to avoid confusion with \(t_5\) or \(t^5\)); | * \(5t\) but not \(t5\) (to avoid confusion with \(t_5\) or \(t^5\)); | ||

* \(x\sqrt{2}\) but not \(\sqrt{2}x\) (to avoid confusion with \(\sqrt{2x}\)). (See [[Something on the right of a radical]]) | * \(x\sqrt{2}\) but not \(\sqrt{2}x\) (to avoid confusion with \(\sqrt{2x}\)). (See [[Something on the right of a radical]]) | ||

* \(\sqrt{2}\sin x\) but not \(\sin x \sqrt{2}\) (to avoid confusion with \(\sin \left(x\sqrt{2}\right)\)). | * \(\sqrt{2}\sin x\) but not \(\sin x \sqrt{2}\) (to avoid confusion with \(\sin \left(x\sqrt{2}\right)\)). (See [[Function application without parentheses]]) | ||

==Addition== | |||

People sometimes rearrange a sum to avoid a leading unary minus, even when this contradicts the convention of writing terms in decreasing order of degree: | |||

\[ 1 - x \] | |||

instead of | |||

\[ -x + 1 \] | |||

==Polynomials== | |||

When writing a polynomial on its own, the usual convention is to write the terms in decreasing order of degree: | |||

\[ x^3 - 32x^2 + 3x -1 \] | |||

But for a series expansion, where higher-order powers are often omitted, it makes more sense to start with the lowest-degree term: | |||

\[ -1 + 3x - 32x^2 + x^3 \] |

## Latest revision as of 13:01, 6 September 2021

When writing an expression that consists of several terms, the conventions regarding their order appear arbitrary.

## Multiplication

It is usual to write:

- \(xy\) and \(yx\) in either order;
- \(5t\) but not \(t5\) (to avoid confusion with \(t_5\) or \(t^5\));
- \(x\sqrt{2}\) but not \(\sqrt{2}x\) (to avoid confusion with \(\sqrt{2x}\)). (See Something on the right of a radical)
- \(\sqrt{2}\sin x\) but not \(\sin x \sqrt{2}\) (to avoid confusion with \(\sin \left(x\sqrt{2}\right)\)). (See Function application without parentheses)

## Addition

People sometimes rearrange a sum to avoid a leading unary minus, even when this contradicts the convention of writing terms in decreasing order of degree:

\[ 1 - x \]

instead of

\[ -x + 1 \]

## Polynomials

When writing a polynomial on its own, the usual convention is to write the terms in decreasing order of degree:

\[ x^3 - 32x^2 + 3x -1 \]

But for a series expansion, where higher-order powers are often omitted, it makes more sense to start with the lowest-degree term:

\[ -1 + 3x - 32x^2 + x^3 \]