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

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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 a term that consists of several factors, the conventions regarding their order appear arbitrary. It is usual to write:
When writing an expression that consists of several terms, the conventions regarding their order appear arbitrary.  


* $xy$ and $yx$ in either order;
 
* $5t$ but not $t5$ (to avoid confusion with $t_5$ or $t^5$);
==Multiplication==
* $x\sqrt{2}$ but not $\sqrt{2}x$ (to avoid confusion with $\sqrt{2x}$).
 
* $\sqrt{2}\sin x$ but not $\sin x \sqrt{2}$ (to avoid confusion with $\sin \left(\sqrt{2}x\right)$).
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:

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:

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