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

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

Revision as of 09:02, 16 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

\[ -x + 1 \]

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:

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