The order of terms matters even when they commute: Difference between revisions
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(The order of factors in a term follows apparently arbitrary conventions.) |
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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; | |||
* \(5t\) 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: | |||
\[ -1 + 3x - 32x^2 + x^3 \] | |||
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:
\[ -1 + 3x - 32x^2 + x^3 \]
