View source for The order of terms matters even when they commute

[[Category:Inconsistencies]]
[[Category:Unspoken conventions]]

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:

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