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

Dual

2023-09-06T08:33:53Z

Mscroggs:

The word "dual" is used to name various similar but different concepts.

* The dual of a polyhedron is the shape obtained by joining the midpoints of all the faces.
* The dual of a function space is the set of all linear functionals on the function space.

[[Category:Ambiguities]]

Dual

2023-09-06T08:33:29Z

Mscroggs:

Dual

2023-09-06T08:33:20Z

Mscroggs: Created page with "The word "dual" is used to name various similar but different concepts. - The dual of a polyhedron is the shape obtained by joining the midpoints of all the faces. - The dual of a function space is the set of all linear functionals on the function space."

The word "dual" is used to name various similar but different concepts.

- The dual of a polyhedron is the shape obtained by joining the midpoints of all the faces.
- The dual of a function space is the set of all linear functionals on the function space.

Apply ... to

2021-09-14T13:05:51Z

Mscroggs: Created page with "Category:Ambiguities Category:Language The sentence "Apply ... to ..." can be ambiguous. For example, "Apply theorem 3 to theorem 6" could mean "apply the statement o..."

[[Category:Ambiguities]]
[[Category:Language]]

The sentence "Apply ... to ..." can be ambiguous. For example, "Apply theorem 3 to theorem 6" could mean "apply the statement of theorem 3 to the statement of theorem 6" or "apply theorems 3, 4, 5 and 6".

Superscript

2021-08-03T14:33:13Z

Mscroggs:

[[Category:Ambiguities]]

Superscripts are most commonly<ref>But there are some other common uses of superscripts, see eg [[powers of trigonometric functions]].</ref> used to denote powers, eg $4^3=64$.

Superscripts are also commonly used to mark footnotes. If there is a footnote about a number, this can lead to an ambiguity, for example: there are 47<ref>This number is a guess, I didn't count them.</ref> pages on this wiki. (Wiki styling puts square brackets around this reference, making this less ambiguous, but this is not always the case elsewhere.)

Superscript

2021-08-03T14:33:03Z

Mscroggs:

[[Category:Ambiguities]]

Superscripts are most commonly<ref>Buy there are some other common uses of superscripts, see eg [[powers of trigonometric functions]].</ref> used to denote powers, eg $4^3=64$.

Superscripts are also commonly used to mark footnotes. If there is a footnote about a number, this can lead to an ambiguity, for example: there are 47<ref>This number is a guess, I didn't count them.</ref> pages on this wiki. (Wiki styling puts square brackets around this reference, making this less ambiguous, but this is not always the case elsewhere.)

Superscript

2021-08-03T14:32:05Z

Mscroggs:

[[Category:Ambiguities]]

Superscripts are most commonly used to denote powers, eg $4^3=64$.

There are some other uses of superscripts, see eg [[powers of trigonometric functions]].

Superscripts are also commonly used to mark footnotes. If there is a footnote about a number, this can lead to an ambiguity, for example: there are 47<ref>This number is a guess, I didn't count them.</ref> pages on this wiki. (Wiki styling puts square brackets around this reference, making this less ambiguous, but this is not always the case elsewhere.)

Superscript

2021-08-03T14:30:27Z

Mscroggs: Created page with "Superscripts are most commonly used to denote powers, eg $4^3=64$. There are some other uses of superscripts, see eg powers of trigonometric functions. Superscripts ar..."

Superscripts are most commonly used to denote powers, eg $4^3=64$.

There are some other uses of superscripts, see eg [[powers of trigonometric functions]].

Superscripts are also commonly used to mark footnotes. If there is a footnote about a number, this can lead to an ambiguity, for example: there are 47<ref>This number is a guess, I didn't count them.</ref> pages on this wiki. (Wiki styling puts square brackets around this reference, making this less ambiguous, but this is not always the case elsewhere.)

Set notation

2021-07-13T12:30:04Z

Mscroggs:

[[Category:Local variations]]
[[Category:Ambiguities]]

When defining a set, something is normally put between curly braces. There are a few different conventions for what can go inside:

* All the elements of the set, separated by commas: $ \{a,b,c, \ldots\} $
* Set-builder notation: a name for a general element of the set, then a condition that all elements must satisfy, with either a vertical bar or a colon in between: $ \{ x \mid P(x) \} $ or $ \{ x : P(x) \} $.

==What goes between braces?==

Piper H asks<ref>[https://twitter.com/pwr2dppl/status/1411816873826697224 tweet by Piper H]</ref>, in the notation $ \{ a_1, a_2, \ldots \} $, where the elements inside are a sequence, are you making an implicit claim that the elements are countable?

[[User:Hpecora1]]: The answer is of course no, this is not a claim of countability. Only well-orderability. This is where the ambiguity lies in the notation above. The length of the sequence is not given, and if the sequence is meant to be interpreted in a ZFC structure, then we need to know explicitly how long this sequence is, i.e. which ordinal indexes its elements. If we don’t, it can represent any nonempty set. (We call this a sequence despite the use of curly braces for an unordered set of elements because the enumeration of elements implies some function mapping ordinals to the $a_i$.

==Colons==

Colons are used in set notation to indicate a condition the elements must satisfy. Colons are also used when defining functions to show which sets a function maps between (eg $f:\mathbb{R}\to\mathbb{R}$. This can cause ambiguities when defining a set containing functions, for example:

$$\{f:\mathbb{R}\to\mathbb{R}:f>0\}$$

==Bars==

Bars can experience issues with ambiguity too, for example:

$$\{a\in\mathbb{R}\mid|a|<2\}$$
$$\{a\in\mathbb{Z}\mid|a|\vert12\}$$

Talk:Ways of writing numbers

2021-07-08T12:01:21Z

Mscroggs:

In the Twitter thread: "Have you seen fractional numbers in hex or octal notation?"
Literals like 0x1.123abcp-5 are now standard in C and C++. The exponent (following 'p') is written in decimal. The Handbook of Floating Point Arithmetic (Muller and about a thousand others) uses this format (sometimes without the 0x) to provide exact floating point constants. -- Unsigned comment by [[User:John McKenna]], 7 July 2021 20:24

Talk:Ways of writing numbers

2021-07-08T12:01:11Z

Mscroggs:

Set notation

2021-07-06T07:48:53Z

Mscroggs:

Lack of brackets in spoken language

2021-07-02T15:45:43Z

Mscroggs:

There are problems similar to those related to [[order of operations]] misunderstandings causes by the lack of brackets in language.

For example, if trying to describe $3^{2x}$, you might say "three to the power of two times x". This could, however, also be interpreted as $2^{3}x$. One common way to reduce the ambiguity is to pause and speed up, ie say "three to the power of [''pause''] two-times-x".

Another example are sentences "17 is a factor of 6 more than 15" and "7 is a factor of 6 more than 15". Both can be interpreted as correct under different readings: 17 is (a factor of 6) more than 15, 7 is a factor of (6 more than 15). The first of these could be disambiguated by saying "17 is 15 plus a factor of 6", but there is no obvious unambiguous candidate for the second.

Matthew Scroggs finds this a particular challenge when writing clues for the [https://chalkdustmagazine.com/regulars/crossnumber Chalkdust crossnumber].

[[Category:Ambiguities]]

Factors

2021-07-02T15:41:40Z

Mscroggs:

The factors of 21 are usually 1, 3, 7, and 21, but sometimes factors is used to describe the number 1, 3, 7 (excluding the number itself).

The proper factors of 21 might be 1, 3, and 7<ref>[https://www.oxfordreference.com/view/10.1093/oi/authority.20110803100349667 Oxford reference: proper factors]</ref>; or 3 and 7<ref>[https://mathworld.wolfram.com/ProperFactor.html Wolfram MathWorld]</ref>.

"Factor" and "divisor" are often used interchangably, but are given distinct meanings by others: [https://mathworld.wolfram.com/ProperFactor.html Wolfram MathWorld] states that proper factors exclude 1 and the number itself, while proper divisors include 1 and exclude the number itself.

There is also inconsistency over whether to include negative numbers as factors or divisors.

[[Category:Ambiguities]]
[[Category:Inconsistencies]]

Factors

2021-07-02T15:38:41Z

Mscroggs: Created page with "The factors of 21 are usually 1, 3, 7, and 21, but sometimes factors is used to describe the number 1, 3, 7 (excluding the number itself. The proper factors of 21 might be 1,..."

The factors of 21 are usually 1, 3, 7, and 21, but sometimes factors is used to describe the number 1, 3, 7 (excluding the number itself.

The proper factors of 21 might be 1, 3, and 7<ref>[https://www.oxfordreference.com/view/10.1093/oi/authority.20110803100349667 Oxford reference: proper factors]</ref>; or 3 and 7<ref>[https://mathworld.wolfram.com/ProperFactor.html Wolfram MathWorld]</ref>.

"Factor" and "divisor" are often used interchangably, but are given distinct meanings by others: [https://mathworld.wolfram.com/ProperFactor.html Wolfram MathWorld] states that proper factors exclude 1 and the number itself, while proper divisors include 1 and exclude the number itself.

There is also inconsistency over whether to include negative numbers as factors or divisors.

[[Category:Ambiguities]]
[[Category:Inconsistencies]]

Lack of brackets in spoken language

2021-07-02T15:25:42Z

Mscroggs:

There are problems similar to those related to [[order of operations]] misunderstandings causes by the lack of brackets in language.

For example, if trying to describe $3^{2x}$, you might say "three to the power of two times x". This could, however, also be interpreted as $2^{3}x$. One common way to reduce the ambiguity is to pause and speed up, ie say "three to the power of [''pause''] two-times-x".

Another example are sentences "17 is a factor of 6 more than 15" and "7 is a factor of 6 more than 15". Both can be interpreted as correct under different readings: 17 is (a factor of 6) more than 15, 7 is a factor of (6 more than 15).

Matthew Scroggs finds this a particular challenge when writing clues for the [https://chalkdustmagazine.com/regulars/crossnumber Chalkdust crossnumber].

[[Category:Ambiguities]]

Lack of brackets in spoken language

2021-07-02T15:24:31Z

Mscroggs: Created page with "There are problems similar to those related to order of operations misunderstandings causes by the lack of brackets in language. For example, if trying to describe \(3^{2..."

There are problems similar to those related to [[order of operations]] misunderstandings causes by the lack of brackets in language.

For example, if trying to describe $3^{2x}$, you might say "three to the power of two times x". This could, however, also be interpreted as $2^{3}x$. One common way to reduce the ambiguity is to pause and speed up, ie say "three to the power of [''pause''] two-times-x".

Another example are sentences "17 is a factor of 6 more than 15" and "7 is a factor of 6 more than 15". Both can be interpreted as correct under different readings: 17 is (a factor of 6) more than 15, 7 is a factor of (6 more than 15).

Matthew Scroggs finds this a particular challenge when writing clues for the [https://chalkdustmagazine.com/regulars/crossnumber Chalkdust crossnumber].

Order of operations

2021-07-02T15:16:16Z

Mscroggs:

There are quite a few mnemonics for the order of operations. A common one in the UK is BODMAS:

* Brackets
* Orders
* Division
* Multiplication
* Addition
* Subtraction

Elsewhere, PEMDAS is popular.

But division and multiplication have equal precedence, and so do addition and subtraction. A common convention is that operations with equal precedence are evaluated from left to right.

This leads to all sorts of misunderstandings.

$ 8 \div 2(1+3) = 16 $ or $ 1 $

Some people think that the presence or omission of a multiplication symbol in the above expression is important: [[Missing multiplication symbol|implicit multiplication]] might bind more tightly than the division symbol.

Several ways of resolving the ambiguity have been suggested, but all the ones [[User:Christian Lawson-Perfect | I've]] seen introduce other problems.

==Suggested resolutions==

'''Reverse Polish Notation''': The expression $(x-2)(x-1)$ would be written instead $\times \, - \, x \, 2 \, - \, x \, 1$, or something like that. There's no need for brackets or operator precedence, but it is hard to see at a glance what each operator applies to.

'''Add brackets''': around everything??

'''Make up a new rule''': At MathsJam Gathering 2020, Christian Lawson-Perfect suggested adding a rule "M before D except after 3". So $6 \div 2 \times 3 = 1$, but $3 \div 2 \times 4 = 6$.

==References==

Christian Lawson-Perfect has made a tool called [https://www.checkmyworking.com/misc/samdob/ SAMDOB] which lets you make up your own mnemonic and see how an expression is evaluated.

Colin Beveridge dubbed viral "puzzles" related to misunderstanding the order of operations [https://www.flyingcoloursmaths.co.uk/new-years-resolution-genius-sic/ fake maths].

Adam Townsend and Matthew Scroggs proposed using [https://chalkdustmagazine.com/blog/medusa-new-bodmas/ MEDUSA] instead of BODMAS to reduce ambiguities caused by division being done before multiplication or subtraction being doing before addition.

[[Category:Ambiguities]]

File talk:Xi bar over Xi .jpg

2021-06-30T14:37:27Z

Mscroggs: Created page with "This, or some variation of it, should be this wiki's logo - ~~~~"

This, or some variation of it, should be this wiki's logo - [[User:Mscroggs|Matthew Scroggs]] ([https://mscroggs.co.uk mscroggs.co.uk]) 14:37, 30 June 2021 (UTC)

Template:Userbox

2021-06-30T14:32:17Z

Mscroggs:

<includeonly>{| style="float: right; margin: 0 0 10px 10px; width: 269px; border-radius: 8px; border: 1px solid #AAAAAA;font-size: 95%;padding: 5px;"
|- style="text-align:center; background-color:#2a4b8d; color: white !important; font-size: 120%"
! colspan=2| '''{{#if:{{{Name|}}}|{{{Name}}}|{{PAGENAME}}}}'''
|-
! colspan=2| [[User_talk:{{PAGENAME}}|Talk]] ~ [[User:{{PAGENAME}}/Sandbox|Sandbox]] ~ [[Special:Contributions/{{PAGENAME}}|Contributions]]{{#if:{{{Website|}}}|<nowiki></nowiki>
{{InfoboxAddrow|rowlabel=Website}}{{#ifeq:{{#explode:{{{Website|}}}|:|0}}|http|[{{{Website|}}} {{#explode:{{{Website|}}}|/|2}}]|{{#ifeq:{{#explode:{{{Website|}}}|:|0}}|https|[{{{Website|}}} {{#explode:{{{Website|}}}|/|2}}]|[http://{{{Website|}}} {{#if:{{{Website name|}}}|{{{Website name}}}|{{{Website}}}}}] |}}}}|}}{{#if:{{{Twitter|}}}|<nowiki></nowiki>
{{InfoboxAddrow|rowlabel=Twitter}}[https://www.twitter.com/{{{Twitter}}} @{{{Twitter}}}]|}}
|}
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You can add this template to your Userpage by writing (for example):

<nowiki>{{Userbox|Name=Chalkdust Magazine|Twitter=chalkdustmag|Website=https://chalkdustmagazine.com}}</nowiki>

</noinclude>

User:Mscroggs

2021-06-30T14:30:45Z

Mscroggs:

{{Userbox|Name=Matthew Scroggs|Twitter=mscroggs|Website=https://mscroggs.co.uk|Website name=mscroggs.co.uk}}

Hello there!

Template talk:Userbox

2021-06-30T14:13:12Z

Mscroggs:

Looks like [https://www.mediawiki.org/wiki/Extension:ParserFunctions ParserFunctions] needs to be installed for stuff like this to work. Until then it looks like the one on [[User:Mscroggs|my userpage]]. - [[User:Mscroggs|Matthew Scroggs]] ([https://mscroggs.co.uk mscroggs.co.uk]) 14:12, 30 June 2021 (UTC)

Template talk:Userbox

2021-06-30T14:12:56Z

Mscroggs: Created page with "Looks like [ParserFunctions https://www.mediawiki.org/wiki/Extension:ParserFunctions] needs to be installed for stuff like this to work. Until then it looks like the one on ..."

Looks like [ParserFunctions https://www.mediawiki.org/wiki/Extension:ParserFunctions] needs to be installed for stuff like this to work. Until then it looks like the one on [[User:Mscroggs|my userpage]]. - [[User:Mscroggs|Matthew Scroggs]] ([https://mscroggs.co.uk mscroggs.co.uk]) 14:12, 30 June 2021 (UTC)

User:Mscroggs

2021-06-30T14:11:16Z

Mscroggs: Created page with "{{Userbox|name=Matthew Scroggs|twitter=mscroggs|website=[https://mscroggs.co.uk mscroggs.co.uk]}} Hello..."

{{Userbox|name=Matthew Scroggs|twitter=mscroggs|website=[https://mscroggs.co.uk mscroggs.co.uk]}}

Hello there!

Template:Userbox

2021-06-30T14:09:41Z

Mscroggs: Created page with "<includeonly>{| style="float: right; margin: 0 0 10px 10px; width: 269px; border-radius: 8px; border: 1px solid #AAAAAA;font-size: 95%;padding: 5px;" |- style="text-align:cent..."

<includeonly>{| style="float: right; margin: 0 0 10px 10px; width: 269px; border-radius: 8px; border: 1px solid #AAAAAA;font-size: 95%;padding: 5px;"
|- style="text-align:center; background-color:#2a4b8d; color: white !important; font-size: 120%"
! colspan=2| '''{{#if:{{{Name|}}}|{{{Name}}}|{{PAGENAME}}}}'''
|-
! colspan=2| [[User_talk:{{PAGENAME}}|Talk]] ~ [[User:{{PAGENAME}}/Sandbox|Sandbox]] ~ [[Special:Contributions/{{PAGENAME}}|Contributions]]{{#if:{{{Website|}}}|<nowiki></nowiki>
{{InfoboxAddrow|rowlabel=Website}}{{#ifeq:{{#explode:{{{Website|}}}|:|0}}|http|[{{{Website|}}} {{#explode:{{{Website|}}}|/|2}}]|{{#ifeq:{{#explode:{{{Website|}}}|:|0}}|https|[{{{Website|}}} {{#explode:{{{Website|}}}|/|2}}]|[http://{{{Website|}}} {{{Website|}}}] |}}}}|}}{{#if:{{{Email|}}}|<nowiki></nowiki>
{{InfoboxAddrow|rowlabel=Email}}[[email::{{{Email}}}| ]][mailto:{{{Email}}} {{{Email}}}]|}}{{#if:{{{Twitter|}}}|<nowiki></nowiki>
{{InfoboxAddrow|rowlabel=Twitter}}[https://www.twitter.com/{{{Twitter}}} @{{{Twitter}}}]|}}
|}
</includeonly><noinclude>
You can add this template to your Userpage by writing (for example):

<nowiki>{{Userbox|name=Chalkdust Magazine|twitter=chalkdustmag|website=https://chalkdustmagazine.com}}</nowiki>

</noinclude>

Template:InfoboxAddrow

2021-06-30T14:09:35Z

Mscroggs: Created page with "|- | style="font-weight: bold" | {{{rowlabel}}} |"

|-
| style="font-weight: bold" | {{{rowlabel}}}
|

LaTeX

2021-06-30T13:33:10Z

Mscroggs: Redirected page to LaTeΧ

#REDIRECT [[LaTeΧ]]

LaTeΧ

2021-06-30T13:32:40Z

Mscroggs: Created page with "The widely used mathematical typesetting language LaTeΧ is written using a capital Greek letter chi as its final letter. In many typefaces, this is indistinguishable from a c..."

The widely used mathematical typesetting language LaTeΧ is written using a capital Greek letter chi as its final letter. In many typefaces, this is indistinguishable from a capital X.

[[Category:Ambiguities]]

Natural numbers

2021-06-30T13:28:53Z

Mscroggs: Created page with "The set of natural numbers, usually written $\mathbb{N}$, sometimes includes 0 and sometimes doesn't include 0. Category:Inconsistencies"

The set of natural numbers, usually written $\mathbb{N}$, sometimes includes 0 and sometimes doesn't include 0.

[[Category:Inconsistencies]]

Matrix indices

2021-06-30T13:26:09Z

Mscroggs: Created page with "It's common to write the entries of a matrix $A$ as $a_{ij}$ without a comma: \(A = \left(\begin{array}{cccc} a_{11}&a_{12}&\dots&a_{1n}\\ a_{21}&a_{22}&\dots&a_{nn}\\ \v..."

It's common to write the entries of a matrix $A$ as $a_{ij}$ without a comma:

$A = \left(\begin{array}{cccc}
a_{11}&a_{12}&\dots&a_{1n}\\
a_{21}&a_{22}&\dots&a_{nn}\\
\vdots&\vdots&\ddots&\vdots\\
a_{n1}&a_{n2}&\dots&a_{nn}
\end{array}\right)$

But it's also common to write the entries of a vector $\mathbf{a}$ as $a_i$:

$\mathbf{a}=\left(\begin{array}{c}a_1\\a_2\\\vdots\\a_n\end{array}\right)$

$a_{12}$ could represent either the entry 1,2 in a matrix, or the 12th entry in a vector. $a_{112}$ could represent a whole range of things.

This is perhaps most ambiguous for expressions like $a_{2n}$ where we could be talking about the $2n$th entries in a vector or an entry in the 2nd row of a matrix.

[[Category:Ambiguities]]