Questions tagged [convention]
Use the convention tag for questions about standard, cultural practices in mathematics.
456 questions
1 vote
0 answers
24 views
Oriented cobordism between knots, direction [closed]
In knot theory, quite often when one defines an oriented cobordism from knot $K_0\subset S^3$ to knot $K_1 \subset S^3$, and draws the picture of the cobordism in $S^3\times [0,1]$, $K_0$ appears to ...
- 11
0 votes
1 answer
176 views
Is the syntax for sequent calculus axioms a pure convention or is there some justification for it?
I am currently studying sequent calculus from Mancosu et al. 2021, chapter 5. The syntax for axioms is given in definition 5.2: $$ A \Rightarrow A $$ Is there some justification for this syntactic ...
- 141
2 votes
1 answer
131 views
Is it possible to legally substitute an element introduced in a definition for a variable in an equation from said definition?
I'm currently studying linear algebra, and in learning about fields, the question expressed in the title of this post came to my mind. The below is a skeleton of the definition I have in my notes for &...
- 23
2 votes
1 answer
106 views
Why does the notation for derivative of a function depend on context?
Recently I have been getting caught up in mathematical notation and how hand-wavy & ambiguous it is in practice. Here is an example of something that troubles me: From what I understand, functions ...
- 43
3 votes
1 answer
145 views
What is the convention for notating geodesics in hyperbolic geometry?
Given the triangle in the Poincare model, would most mathematicians notate a side of the triangle $\overline{\text{BC}}$ or ? Basically, is there a standard convention based on function/visual ...
- 303
0 votes
1 answer
94 views
Are both $a_n\le b_n\le c_n$ and $a_n\ge b_n\ge c_n$ equivalent statements of the squeezing theorem for sequences?
I think the answer to this is yes. But I am seeking confirmation as my concern is that I can only find the version, $a_n\le b_n\le c_n$, such as this Wikipedia page each time I search online. Here is ...
- 529
9 votes
1 answer
125 views
Order of adjectival properties
In mathematics, how should the adjectives in front of a noun be ordered? Are there conventions? I can think of a few practices: Use stronger adjectives or more specialised properties first, and more ...
- 736
3 votes
0 answers
83 views
Could roots with an odd index and a negative radicand be real numbers?
Hello everyone, I'm a student in the 1st grade of high school, and I want to make it clear from the beginning that I have no advanced knowledge of mathematics. In our algebra class, I asked the ...
0 votes
0 answers
44 views
Naming convention for PDE operator.
This question is about naming conventions. Consider a partial differential equation (PDE) in $u$ of the form $$u(t,x) = L(t,x,u,u',u'',\ldots)$$ I am interested if there is a usual name for the ...
- 584
0 votes
0 answers
74 views
Where does the convention for the letter $W$ for Coxeter groups come from?
We often use special letters for certain groups like $D$ for Dihedral groups, or $S$ for Symmetric groups. I was wondering why it is a convention to use the letter $W$ for Coxeter groups. I can ...
- 612
2 votes
1 answer
261 views
Why is it "polynomial in x" instead of "polynomial of x"? Doubt regarding convention. [closed]
I've often seen the phrase "a polynomial in $x$" used in textbooks and papers, especially in formal or algebraic contexts. But in more casual or introductory settings, people often say "...
0 votes
1 answer
76 views
Why opposite notations for polynomial basis representation in Algebra (Fields) as compared to that in Coding theory?
In books on Fields, an extension field polynomial representation uses the notation where right most bit is considered as $a_0$ & left most is $a_{n-1}$ For e.g. in $F_{2^4}$ $11 = 1,0,1,1 = x^3 + ...
- 662
0 votes
2 answers
87 views
When do we specify domains when it's implied?
I asked an AI about the language a^m b^n c^n d^m, and in replying to me, it translated that into $\{a^mb^nc^nd^m \mid m, n \geq 0\}$. Is this standard usage? I find it weird; negative integers make no ...
- 123
0 votes
2 answers
337 views
Elementary question: something feels missing in the "domain, range, codomain" terminology in describing a function.
A basic description of a function is this: $$f: \text{dom}(f) \subseteq \mathbb{R}^n \to \text{ran}(f) \subseteq \mathbb{R}^m$$ Clearly, this function has FOUR things going on: Domain: $\text{dom}(f)...
- 8,711
2 votes
1 answer
194 views
Is this an equivalent definition of BMO?
On a metric space equipped with a Borel measure where balls have positive and finite measure, a function $f\in L^1_{\rm loc}$ is said to be in BMO if \begin{equation*} \exists C \: \text{ such that} \:...
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