Why start at x, y, z - User contributions [en-gb]

Asymmetry of significant figures

2022-09-27T20:45:02Z

ColinBeveridge: Add Tom Bowler reference

[[Category:Unpleasantness]]

The bounds on a value given to a number of significant figures are not symmetric when the value given is a power of 10.

For example, if $ x = 1000 $ to two significant figures, then $ 995 \le x \lt 1050 $. The lower bound is 5 smaller than 1000, while the upper bound is 50 larger.

Tom Bowler led a [https://twitter.com/Ridermeister/status/1574441481892499458 twitter discussion on a related topic].

Asymmetry of significant figures

2022-09-27T20:42:35Z

ColinBeveridge: Create page

The order of terms matters even when they commute

2021-07-15T08:42:54Z

ColinBeveridge: Brackets not dollars.

[[Category:Inconsistencies]]

When writing a term that consists of several factors, the conventions regarding their order appear arbitrary. 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 $\sqrt{2x}$).
* $\sqrt{2}\sin x$ but not $\sin x \sqrt{2}$ (to avoid confusion with $\sin \left(x\sqrt{2}\right)$).

The order of terms matters even when they commute

2021-07-15T08:41:23Z

ColinBeveridge: The order of factors in a term follows apparently arbitrary conventions.

[[Category:Inconsistencies]]

When writing a term that consists of several factors, the conventions regarding their order appear arbitrary. 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 $\sqrt{2x}$).
* $\sqrt{2}\sin x$ but not $\sin x \sqrt{2}$ (to avoid confusion with $\sin \left(\sqrt{2}x\right)$).

Mixed fractions

2021-06-30T12:52:40Z

ColinBeveridge: Created page with "Category:Inconsistencies Adjacency means different things depending on the context: * $ 2x $ means $ 2 \times x$. * $ 2 \frac{2}{3} $ means $ 2 + \frac{2}{3}$...."

[[Category:Inconsistencies]]

Adjacency means different things depending on the context:

* $ 2x $ means $ 2 \times x$.
* $ 2 \frac{2}{3} $ means $ 2 + \frac{2}{3}$.

This results in the coincidence $ \sqrt{2 \frac{2}{3}} = 2 \sqrt{\frac{2}{3}} $.

Stacked fractions

2021-06-30T12:42:14Z

ColinBeveridge:

[[Category:Ambiguities]]

A fraction written on multiple levels is often ambiguous, especially when handwritten. For example, $\frac{10}{\frac{2}{5}}$ and $\frac{\frac{10}{2}}{5}$ result in 25 and 1, respectively.

Stacked fractions

2021-06-30T12:40:55Z

ColinBeveridge: Created page with "A fraction written on multiple levels is often ambiguous, especially when handwritten. For example, $\frac{10}{\frac{2}{5}}$ and $\frac{\frac{10}{2}}{5}$ result in 25 and..."

A fraction written on multiple levels is often ambiguous, especially when handwritten. For example, $\frac{10}{\frac{2}{5}}$ and $\frac{\frac{10}{2}}{5}$ result in 25 and 1, respectively.