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

Lack of brackets in spoken language

2021-07-02T16:12:59Z

Adam Atkinson:

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 \(3^{2}x\). 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]]

Main Page

2021-07-01T12:06:59Z

Adam Atkinson:

[[Category:Admin]]

This is a collection of ambiguous, inconsistent, or just unpleasant conventions in mathematical notation.

For each bit of notation, I want to collect examples, alternatives, and references to discussions about them.

The site's name is a reference to the question about why we start naming variables at \(x\).

You can edit this site, once you've [[Special:CreateAccount|created an account]].

[[References|Useful references]]

==Categories==

* [[:Category:Inconsistencies]]
* [[:Category:Ambiguities]]
* [[:Category:Unpleasantness]]
* [[:Category:Conflicting definitions]]

Positive-and-Negative

2021-06-30T17:39:34Z

Adam Atkinson:

[[Category:Inconsistencies]]

In many countries, 0 is neither positive nor negative.

In France, it is both. If there are any other places where this holds, someone will probably edit this line.

Positive-and-Negative

2021-06-30T17:18:56Z

Adam Atkinson: Created page with "Category:Inconsistencies In many countries, 0 is neither positive nor negative. In France, it is both."

[[Category:Inconsistencies]]

In many countries, 0 is neither positive nor negative.

In France, it is both.

Whole numbers

2021-06-30T17:17:40Z

Adam Atkinson:

"Whole numbers" are often referred to without being defined, since many people think everyone knows what they are.

However, there are at least three things people mean by the term.

* Positive integers
* Non-negative integers
* Integers

If you are French, the above is still true but the meanings of two of the entries are swapped, which ends up making no difference.

It is possible to find maths homeworks on the web where students are asked which numbers on a list are whole numbers, and to find model answers where, for example, -3 is not one.

If you say "whole numbers", it may be best to say what you mean by it. Or don't use it at all.

It's quite easy to find books which use the term without defining it explicitly. If someone says the powers of x in a polynomial have to be whole numbers, that's a pretty good clue as to what they think it means.

[[Category:Inconsistencies]]

Division

2021-06-30T17:15:27Z

Adam Atkinson:

[[Category:Inconsistencies]]

In some countries, the symbol you don't use for division if you're over about 13 years old is ":". In others, the symbol you don't use for division if you're over about 13 years old is "÷". Unless you have children or work in a school you might never notice this difference.

Here we see Maurizio Codogno having to explain to his readers what ÷ means:

https://www.ilpost.it/mauriziocodogno/2019/08/12/ma-ci-importa-sapere-quanto-fa-8%C3%B7222/

Division

2021-06-30T17:13:39Z

Adam Atkinson: Created page with "In some countries, the symbol you don't use for division if you're over about 13 years old is ":". In others, the symbol you don't use for division if you're over about 13 yea..."

In some countries, the symbol you don't use for division if you're over about 13 years old is ":". In others, the symbol you don't use for division if you're over about 13 years old is "÷".

Here we see Maurizio Codogno having to explain to his readers what ÷ means:

https://www.ilpost.it/mauriziocodogno/2019/08/12/ma-ci-importa-sapere-quanto-fa-8%C3%B7222/

Mixed fractions

2021-06-30T17:09:30Z

Adam Atkinson:

[[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 \( \sqrt{2 \frac{2}{3}} = 2 \sqrt{\frac{2}{3}} \).

Adam Atkinson says that mixed fractions aren't understood everywhere, which prompted Christian Lawson-Perfect to run a survey on whether they exist<ref>[https://aperiodical.com/2016/09/do-you-use-mixed-fractions/ Do you use mixed fractions?]</ref>. At least one respondent asked "Are there really countries where this notation is not used?" and at least one respondent asked "Are there really countries where this notation is used?".

Our best information is that France, Spain, Italy and Portugal are unmixed. Though it is hard to reconcile this with mixed numbers appearing on the syllabus for a particular age range on the Portuguese Ministry of Education web page. Or with their presence in at least some Italian middle school textbooks. Note that even Italian middle school teachers who believe mixed numbers exist may not believe that negative mixed numbers exist or what they might mean if they did.

For the record,

*\(-1 \frac{1}{4}\) means \(-\frac{5}{4}\) in mixed countries

So saying "mixed numbers have an invisible plus in them" is not the way to explain them.

Adam Atkinson talks about Italy and mixed numbers here <ref>[https://www.youtube.com/watch?v=BGk4kVactWU Mixed numbers]</ref> but this only begins to convey how confusing the situation is if you ask multiple people from the same notionally unmixed country about them. He has been told _authoritatively_ that Belgium is and is not mixed and has no idea what to believe.

==References==
<references/>

Mixed fractions

2021-06-30T17:07:32Z

Adam Atkinson:

[[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 \( \sqrt{2 \frac{2}{3}} = 2 \sqrt{\frac{2}{3}} \).

Adam Atkinson says that mixed fractions aren't understood everywhere, which prompted Christian Lawson-Perfect to run a survey on whether they exist<ref>[https://aperiodical.com/2016/09/do-you-use-mixed-fractions/ Do you use mixed fractions?]</ref>.

Our best information is that France, Spain, Italy and Portugal are unmixed. Though it is hard to reconcile this with mixed numbers appearing on the syllabus for a particular age range on the Portuguese Ministry of Education web page. Or with their presence in at least some Italian middle school textbooks. Note that even Italian middle school teachers who believe mixed numbers exist may not believe that negative mixed numbers exist or what they might mean if they did.

For the record,

*\(-1 \frac{1}{4}\) means \(-\frac{5}{4}\) in mixed countries

So saying "mixed numbers have an invisible plus in them" is not the way to explain them.

Adam Atkinson talks about Italy and mixed numbers here <ref>[https://www.youtube.com/watch?v=BGk4kVactWU Mixed numbers]</ref> but this only begins to convey how confusing the situation is if you ask multiple people from the same notionally unmixed country about them. He has been told _authoritatively_ that Belgium is and is not mixed and has no idea what to believe.

==References==
<references/>

Mixed fractions

2021-06-30T17:06:48Z

Adam Atkinson:

[[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 \( \sqrt{2 \frac{2}{3}} = 2 \sqrt{\frac{2}{3}} \).

Adam Atkinson says that mixed fractions aren't understood everywhere, which prompted Christian Lawson-Perfect to run a survey on whether they exist<ref>[https://aperiodical.com/2016/09/do-you-use-mixed-fractions/ Do you use mixed fractions?]</ref>.

Our best information is that France, Spain, Italy and Portugal are unmixed. Though it is hard to reconcile this with mixed numbers appearing on the syllabus for a particular age range on the Portuguese Ministry of Education web page. Or with their presence in at least some Italian middle school textbooks. Note that even Italian middle school teachers who believe mixed numbers exist may not believe that negative mixed numbers exist or what they might mean if they did.

For the record,

*\(-1 \frac{1}{4}\) means \(-\frac{5}{4}\) in mixed countries

Adam Atkinson talks about Italy and mixed numbers here <ref>[https://www.youtube.com/watch?v=BGk4kVactWU Mixed numbers]</ref> but this only begins to convey how confusing the situation is if you ask multiple people from the same notionally unmixed country about them. He has been told _authoritatively_ that Belgium is and is not mixed and has no idea what to believe.

==References==
<references/>

Mixed fractions

2021-06-30T17:06:33Z

Adam Atkinson:

[[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 \( \sqrt{2 \frac{2}{3}} = 2 \sqrt{\frac{2}{3}} \).

Adam Atkinson says that mixed fractions aren't understood everywhere, which prompted Christian Lawson-Perfect to run a survey on whether they exist<ref>[https://aperiodical.com/2016/09/do-you-use-mixed-fractions/ Do you use mixed fractions?]</ref>.

Our best information is that France, Spain, Italy and Portugal are unmixed. Though it is hard to reconcile this with mixed numbers appearing on the syllabus for a particular age range on the Portuguese Ministry of Education web page. Or with their presence in at least some Italian middle school textbooks. Note that even Italian middle school teachers who believe mixed numbers exist may not believe that negative mixed numbers exist or what they might mean if they did.

For the record,

*\-1 \frac{1}{4}\) means \(-\frac{5}{4}\) in mixed countries

Adam Atkinson talks about Italy and mixed numbers here <ref>[https://www.youtube.com/watch?v=BGk4kVactWU Mixed numbers]</ref> but this only begins to convey how confusing the situation is if you ask multiple people from the same notionally unmixed country about them. He has been told _authoritatively_ that Belgium is and is not mixed and has no idea what to believe.

==References==
<references/>

Mixed fractions

2021-06-30T17:02:55Z

Adam Atkinson:

[[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 \( \sqrt{2 \frac{2}{3}} = 2 \sqrt{\frac{2}{3}} \).

Adam Atkinson says that mixed fractions aren't understood everywhere, which prompted Christian Lawson-Perfect to run a survey on whether they exist<ref>[https://aperiodical.com/2016/09/do-you-use-mixed-fractions/ Do you use mixed fractions?]</ref>.

Our best information is that France, Spain, Italy and Portugal are unmixed. Though it is hard to reconcile this with mixed numbers appearing on the syllabus for a particular age range on the Portuguese Ministry of Education web page. Or with their presence in at least some Italian middle school textbooks. Note that even Italian middle school teachers who believe mixed numbers exist may not believe that negative mixed numbers exist or what they might mean if they did.

Adam Atkinson talks about Italy and mixed numbers here <ref>[https://www.youtube.com/watch?v=BGk4kVactWU Mixed numbers]</ref> but this only begins to convey how confusing the situation is if you ask multiple people from the same notionally unmixed country about them. He has been told _authoritatively_ that Belgium is and is not mixed and has no idea what to believe.

==References==
<references/>

Mixed fractions

2021-06-30T16:59:00Z

Adam Atkinson:

[[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 \( \sqrt{2 \frac{2}{3}} = 2 \sqrt{\frac{2}{3}} \).

Adam Atkinson says that mixed fractions aren't understood everywhere, which prompted Christian Lawson-Perfect to run a survey on whether they exist<ref>[https://aperiodical.com/2016/09/do-you-use-mixed-fractions/ Do you use mixed fractions?]</ref>.

Our best information is that France, Spain, Italy and Portugal are unmixed. Though it is hard to reconcile this with mixed numbers appearing on the syllabus for a particular age range on the Portuguese Ministry of Education web page. Or with their presence in at least some Italian middle school textbooks.

Adam Atkinson talks about Italy and mixed numbers here <ref>[https://www.youtube.com/watch?v=BGk4kVactWU Mixed numbers]</ref> but this only begins to convey how confusing the situation is if you ask multiple people from the same notionally unmixed country about them. He has been told _authoritatively_ that Belgium is and is not mixed and has no idea what to believe.

==References==
<references/>

Whole numbers

2021-06-30T16:53:31Z

Adam Atkinson:

"Whole numbers" are often referred to without being defined, since many people think everyone knows what they are.

However, there are at least three things people mean by the term.

Positive integers
Non-negative integers
Integers

It is possible to find maths homeworks on the web where students are asked which numbers on a list are whole numbers, and to find model answers where, for example, -3 is not one.

If you say "whole numbers", it may be best to say what you mean by it. Or don't use it at all.

It's quite easy to find books which use the term without defining it explicitly. If someone says the powers of x in a polynomial have to be whole numbers, that's a pretty good clue as to what they think it means.

[[Category:Inconsistencies]]

Whole numbers

2021-06-30T16:52:49Z

Adam Atkinson:

"Whole numbers" are often referred to without being defined, since many people think everyone knows what they are.

However, there are at least three things people mean by the term.

Positive integers
Non-negative integers
Integers

It is possible to find maths homeworks on the web where students are asked which numbers on a list are whole numbers, and to find model answers where, for example, -3 is not one.

If you say "whole numbers", it may be best to say what you mean by it. Or don't use it at all.

It's quite easy to find books which use the term without defining it explicitly. If someone says the powers of x in a polynomial have to be whole numbers, that's a pretty good clue as to what they think it means.

[[Category:Ambiguities]]

Whole numbers

2021-06-30T16:47:15Z

Adam Atkinson: Created page with ""Whole numbers" are often referred to without being defined, since many people think everyone knows what they are. However, there are at least three things people mean by the..."

"Whole numbers" are often referred to without being defined, since many people think everyone knows what they are.

However, there are at least three things people mean by the term.

Positive integers
Non-negative integers
Integers

It is possible to find maths homeworks on the web where students are asked which numbers on a list are whole numbers, and to find model answers where, for example, -3 is not one.

If you say "whole numbers", it may be best to say what you mean by it. Or don't use it at all.

It's quite easy to find books which use the term without defining it explicitly. If someone says the powers of x in a polynomial have to be whole numbers, that's a pretty good clue as to what they think it means.