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

From Why start at x, y, z
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[[Category:Inconsistencies]]
[[Category:Inconsistencies]]


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.  
 
 
==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

\[ -x + 1 \]