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

From Why start at x, y, z
m
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
[[Category:Inconsistencies]]
[[Category:Inconsistencies]]
[[Category:Unspoken conventions]]


When writing an expression that consists of several terms, the conventions regarding their order appear arbitrary.  
When writing an expression that consists of several terms, the conventions regarding their order appear arbitrary.  
Line 11: Line 12:
* \(5t\) 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==
==Addition==
Line 22: Line 23:


\[ -x + 1 \]
\[ -x + 1 \]
==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:

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