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

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m (Christian Lawson-Perfect moved page The order of factors matters even when they commute to The order of terms matters even when they commute) |
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[[Category:Inconsistencies]] | [[Category:Inconsistencies]] | ||

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; | ||

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* \(x\sqrt{2}\) 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 \(\sin \left(x\sqrt{2}\right)\)). | ||

==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 | |||

\[ -x + 1 \] |

## Revision as of 09:39, 15 July 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 \(\sin \left(x\sqrt{2}\right)\)).

## 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

\[ -x + 1 \]