Tagged Questions
1
vote
0answers
21 views
Notation for Restriction of Permutation
Suppose $\sigma$ and $\tau$ are permutations such that $\sigma(x)\not=x\implies \sigma(x)=\tau(x)$. Intuitively, I would like to think of $\sigma$ as a restriction (or projection) of $\tau$ onto a ...
3
votes
2answers
62 views
A question on notation for open sets
Yesterday I was presenting a seminar where I started using this notation to make sentences shorter; whenever I wanted to say that $A$ was open in $B$, I would write $A\underset{op}\subset B$, with the ...
6
votes
1answer
215 views
Is there a rigorous theory of context, whereby sets can gain additional structure within a context?
Consider sets $G$ and $H$ and a function $f : G \rightarrow H$. So far, it doesn't really make sense to ask whether $G$ and $H$ are groups (technically, the answer is "no, they're not groups"), and ...
3
votes
0answers
48 views
Why is the Euclidean metric called the prime at infinity?
I've been studying p-adic analysis recently and after a bit of searching on the web, I haven't found an answer as to why the Euclidean metric is referred to as the 'prime at infinity', and given the ...
3
votes
4answers
119 views
Sequence Notation — Which brackets to use?
I'm teaching sequences at the moment. I've always put sequences in round brackets, for example $(1,2,3,4,5)$ is a sequence whose first member is $1$, whose second member is $2$, and so on. I've also ...
0
votes
5answers
75 views
Super or subscript notation on the left hand side of a symbol?
Are there any commonly used notations with super or subscripts on the left hand side of the symbol? or on both sides of a symbol? If so, then what is the latex for having sup/sub script on left or ...
2
votes
2answers
52 views
Why is $S/R$ a ring extension?
If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
0
votes
0answers
22 views
Standard notation for the the collection of all *minimal* elements of the set of all upper bounds?
Let $(P,\leq)$ denote a poset and suppose $X \subseteq P$. Then the minimum element of the set of all upper bounds of $X$ can be denoted $\operatorname{sup} X$, or $\bigvee X$. Is there a similar ...
6
votes
0answers
113 views
Is there a collection of alternative mathematical notation? (Semi-soft Question)
I'm interested in alternative systems of notation for mathematics. I've often heard how mathematical notation is illogical, inconsistent, filled with grandfather clauses that serve no purpose, and ...
12
votes
1answer
205 views
The double factorial notation
The double factorial is defined as
$$n!! = \begin{cases} n \cdot (n-2) \cdot (n-4) \cdots 3 \cdot 1 = \dfrac{(n+1)!}{2^{(n+1)/2}((n+1)/2)!} & \text{ If $n \in \mathbb{Z}^+$, is odd}\\
n \cdot ...
11
votes
1answer
214 views
The Gamma function and the Pi function
I have been studying differential equation, in particular special functions.
Euler's Gamma function, and Gauss's Pi function are essentially the same, differing only by an offset of one unit.
for ...
33
votes
7answers
2k views
Why is 'abuse of notation' tolerated?
I've personally tripped up on a few concepts that came down to an abuse of notation, and I've read of plenty more on stack exchange. It seems to all be forgiven with a wave of the hand. Why do we ...
1
vote
2answers
75 views
What does means the $\frown$ in sequence notation?
In the theorem 3.6 of Juhász's Cardinal Functions in General Topology appears the following symbol about sequence: $\frown$
The role context of it's appearance is the following:
Theorem. Let X be an ...
1
vote
2answers
190 views
Is there a Math symbol that means “associated”
I am looking for a Math symbol that means "associated" and I don't mean "associated" as something as complicated as isomorphism or anything super fancy.
I am looking for a symbol that means ...
4
votes
5answers
481 views
Why do mathematicians use this symbol $\mathbb R$ to represent the real numbers?
So, I'm wondering why mathematicians use the symbols like $\mathbb R$, $\mathbb Z$, etc... to represent the real and integers number for instance. I thought that's because these sets are a kind of ...
