Wikipedia:Reference desk/Mathematics

Welcome to the mathematics section
of the Wikipedia reference desk.

skip to bottom

Select a section:

• Computing
• Entertainment
• Humanities
• Language
• Mathematics
• Science
• Miscellaneous
• Archives

Want a faster answer?

Main page: Help searching Wikipedia

   

How can I get my question answered?

• Select the section of the desk that best fits the general topic of your question (see the navigation column to the right).
• Post your question to only one section, providing a short header that gives the topic of your question.
• Type '~~~~' (that is, four tilde characters) at the end – this signs and dates your contribution so we know who wrote what and when.
• Don't post personal contact information – it will be removed. Any answers will be provided here.
• Please be as specific as possible, and include all relevant context – the usefulness of answers may depend on the context.
• Note:
  • We don't answer (and may remove) questions that require medical diagnosis or legal advice.
  • We don't answer requests for opinions, predictions or debate.
  • We don't do your homework for you, though we'll help you past the stuck point.
  • We don't conduct original research or provide a free source of ideas, but we'll help you find information you need.

Ready? Ask a new question!

How do I answer a question?

Main page: Wikipedia:Reference desk/Guidelines

• The best answers address the question directly, and back up facts with wikilinks and links to sources. Do not edit others' comments and do not give any medical or legal advice.

See also:

• Teahouse
• Help desk
• Village pump
• Help manual

February 2

English

What is noun phrase — Preceding unsigned comment added by Ibrahim shaaibu (talk • contribs) 01:30, 2 February 2022 (UTC)

This is really a question for the Language section, but see our Noun phrase article. All noun phrases in the following lines are underlined:

Twinkle, twinkle, little star,

How I wonder what you are!

Up above the world so high,

Like a diamond in the sky.

The noun phrase in the last line contains two embedded noun phrases: a diamond and the sky.  --Lambiam 02:44, 2 February 2022 (UTC)

February 3

Definition of a topological space by neighborhoods

In the article on "topological space" the section Definition by Neighborhoods lists four axioms. I don't see how axiom 4 is independent.

Axiom 1 says: If N is a neighborhood of point x, then x is an element of N.

Axiom 4 says: If N is a neighborhood of point x, then N contains a neighborhood M of x such that N is a neighborhood of every point in M.

Doesn't 4 follow directly from 1? The singleton set containing only the point x is a subset of every neighborhood of x, so it always satisfies the conditions for neighborhood M in 4.

What am I missing here? Can you point me to a description of axiom 4 that I can understand without a deep background in topology? — Preceding unsigned comment added by Bronco creek (talk • contribs) 19:01, 3 February 2022 (UTC)

What you're missing is that the singleton {x} might not be a neighborhood of x. --Trovatore (talk) 19:09, 3 February 2022 (UTC)

Thanks. That'll teach me to trust my intuition. — Preceding unsigned comment added by Bronco creek (talk • contribs) 19:54, 3 February 2022 (UTC)

The key is not so much not to trust intuition, as to get a more trustworthy intuition.

Intuition is fundamental to mathematics. You simply can't do anything nontrivial without it. But you have to develop it. And you have to keep testing it, looking for places where it doesn't serve you well, and be willing to change those.

In this particular case, the intuition that might have served you is that a neighborhood is a set that contains a given point, plus a little margin around it. That ordinarily rules out singletons. Note that it doesn't always rule out singletons, but that's the base case you can have in mind, being aware of exceptions. --Trovatore (talk) 20:19, 3 February 2022 (UTC)

The key is not so much not to trust intuition, as to get a more trustworthy intuition. Words to live by. --RDBury (talk) 22:58, 3 February 2022 (UTC)

February 7

Height of Simplexes

I'm working my way through Simplex and have been unable to find exactly what the height of each simplex is. I'm defining the "height" of an n-simplex as the distance from one vertex to the center of the n-1 simplex made up of the other vertices. So the "Height" of a 2-simplex is sqrt(3)/2. and the "Height" of a 3-simplex is sqrt(6)/3 (according to Tetrahedron). I'm presuming that they tend to 0 as n goes to infinity, but I don't know if there is an easy formula.Naraht (talk) 09:37, 7 February 2022 (UTC)

That obviously depends on the choice of a vertex, as in 2D example you may have three different heights of a triangle, depending on a vertex chosen as an apex. --CiaPan (talk) 10:21, 7 February 2022 (UTC)

I think we are assuming that it is the "standard simplex", which will be symmetric with respect to choice of vertex. See a discussion here: https://math.stackexchange.com/questions/1697870/height-of-n-simplex showing that this height is ${\sqrt {\frac {n+1}{2n}}}$. Your answer is different I guess because you assumed the simplex edge length is 1? The typical construction of the standard simplex makes the edge length ${\sqrt {2}}$. Staecker (talk) 12:34, 7 February 2022 (UTC)