# Tagged Questions

26 views

### Is there a conventional symbol for the set of radical expressions?

There is already a question about the name of such a set: Name for numbers expressible as radicals My question is related. The rational complex numbers might be denoted ℚ(i), and the algebraic ...
27 views

### What is an open property?

From an academic paper, "the existence of elliptic or hyperbolic 2-periodic orbits is an open property". I have never seen the term "open property" used before, moreover the paper gives no ...
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### How are the essential upper and lower limits defined?

What means $$\operatorname*{ess\,lim\,inf}_{x\to x^*} F(x)$$ and $$\operatorname*{ess\,lim\,sup}_{x\to x^*} F(x)?$$ Sorry I also do not know in ...
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### Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$, how to call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$?

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$ How do people call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$? Sum of positive components of $X$? The positive semi definite part of $X$? ...
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### In regards to metric spaces, does $d^\star$ have an accepted name, or notation? Do any authors use it?

(I write $\omega$ for the set $\{0,1,2,\ldots\}$.) Let $X$ denote a metric space with metric $d$. Define a function $d^{\star} : X^\omega \times X^\omega \rightarrow [0,\infty]^\omega$ by writing ...
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### Alternatives to the notation $\|x\|$ for the norm of $x$?

For aesthetic reasons, I don't like the notation $\|x\|$ for the norm of $x$. Have any alternatives been proposed?
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### Cone of convex solutions

I have been reading a paper, on monge-ampere type equations, and the existence of a unique convex solution has been proven to exist in $C^{3,\alpha}(\Omega)\cap C^{2,\alpha}(\overline{\Omega})$, for ...
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### History of notation: “!”

Does anyone know where the factorial "!" symbol came from? I can't decide if it is my favorite or least favorite notation in mathematics...
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### Question about definition of some classes of bimodules.

Suppose that we have a ring $R$ and a $R$-$R$ bimodule $M$ such that: For every $r\in R$ and $m\in M$ there exists $r'\in R$ such that $m\cdot r=r'\bullet m.$ Examples of this bimodules can be seen ...
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### First usage of the symbol ∈

Concerning a book [1] I am reading the symbol $\in$ was first used by Giuseppe Peano and is the first letter $\epsilon$ (epsilon) of the word ἐστί (means "is"). Does anyone know in which work of Peano ...
350 views

### What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
125 views

### Commutator subgroup - or?

If $G$ is a group and $X, Y \subseteq G$ then the commutator subgroup of $G$ is defined as $[G, G] = \langle [x, y] \mid x, y\in G \rangle$, where $[x, y] = x^{-1}y^{-1}xy$ and the group generated by ...
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### Notation to refer to all the n element subsets of a set?

Is there a notation to refer to all the n element subsets of a set? I know the power set denotes all of the subsets.
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### What is P(Y) here?

A multivalued map, f: X -> Y, from a set X to a set Y, is a map f: X -> P(Y). Multivalued maps will be also called multimaps. I don't understand what a multimap is in category theory and I think the P ...
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### Notation for a function that is invertible only in 1 variable

I have not yet seen something similar before. Let $f:D\times [0,1]\to \mathbb{R}$ be a function, and for every $x\in D\subset\mathbb{R}^n$ the function $f(x,s)$ is increasing in $s$. In other words: ...
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Note: I've substantially edited the definition; $f$ is now allowed to be a functor. Given categories $\mathcal{C}$ and $\mathcal{D}$, we can form the functor category $[\mathcal{C},\mathcal{D}]$. Now ...
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### $\sin^2$ notation and uses of the alternative.

So I was taking my calculus class and I was shocked by the following: Apparently its a convention for $\sin^2(\alpha)=(\sin(\alpha))^2$ As opposed to what I thought made more sense which was ...
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### Category of topological pairs

Is there a standard abbreviation for the category of topological pairs? I have searched for it in vain.
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### “Preimage” of a binary relation

Consider the binary relation $R \subseteq X \times Y$. Is there a standard name and notation for the set $X' = \{x\ |\ (x, y) \in R\}$? ProofWiki calls $X'$ the preimage of $R$, denoted as ...
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### Reference request: Integrals involving $[x]$, $\{x\}$, $d[u]$, $d\{u\}$

I would appreciate reference suggestions to learn how to deal with integrals involving $[x]$, $\{x\}$, $d[u]$, and $d\{u\}$. Thanks!
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### How can i learn to use $\LaTeX$? [closed]

Could you recommend any websites or books or resources for me to learn how to use $\LaTeX$? I've asked many real analysis question recently by uploading images and some people suggested I should use ...
55 views

### What does $K^{1/p}$ for a field $K$ mean?

In the proof of the finite generation of the invariant ring of a finite group acting on $k[x_1,\dots,x_n]$, at one time there is a symbol I don't understand. The situation is as follows. $k$ is a ...
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### Modern approaches to mathematical notation

I'm interested if there is literature on projects which try to improve formal notation, especially for doing mathematics on an advanced level. For example, I'm thinking along the lines of diagrammatic ...
103 views

### Is the variant direct image mathematically significant?

Preimages have the property that for an arbitrary function $f : X \rightarrow Y$ and all $B \subseteq Y$ it holds that $$f^{-1}(B^c)=[f^{-1}(B)]^c.$$ However, the analogous statement for direct ...
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### Should I put interpunction after formulas?

I am presently doing my first substantial piece of mathematical writing, hence this, probably somewhat silly, question. How does display-style mathematics interact with punctuation? More ...
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### Is there a common notation for the labelled degree of a vertex?

Let $G$ be an undirected graph with labelled edges. The labelled degree of a vertex $v \in V(G)$ is the number of edges incident to $v$ with distinct labels. The definition of the labelled degree ...
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### What are $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$?

Sometimes reading on wikipedia or in this site (and in very different context like topology, arithmetic and logic) I have found these symbols $\Sigma _n^i$, $\Pi _n^i$ and $\Delta _n^i$. They are ...
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### 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 ...
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### Diagrammatic (Postfix) Composition of Functions

Consider the functions $f : X \to Y$ and $g : Y \to Z$. According to the Wikipedia articles on Function Composition, the application of $f$ to an input $x$ can be written as $xf$ (as opposed to the ...
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### 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. ...
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### Enumeration of symbols in grammatical expressions or vertices in tree graphs

I have expressions (type of a function) like e.g. $$f:(A\to B)\to C \to (D\to E)\to F.$$ (Where I understand $A\to B\to C$ as $A\to (B\to C)$, in case that is relevant.) There might be information ...
208 views

### Generalization of a product measure

Let $(X,\mathfrak B(X))$ and $(Y,\mathfrak B(Y))$ be measurable spaces and further let $\mu$ be a measure on $\mathfrak B(X)$ and let $K$ be a kernel, i.e. for any $x\in X$ we have $K_x$ is a measure ...
228 views

### Inverse function notation

Suppose $f$ and $g$ are functions that fail to be one-to-one, but $f+g$ is one-to-one. Has anyone ever seen the notation $(f+g)^{-1}$ for the inverse function in that situation? (I find myself ...
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In Godel's Incompleteness Theorem, his theorem is about a system of logic. Where can I find more about this study, especially the notation? EDIT I mean logic about systems in general. I worded the ...
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### Original papers on the subject of group actions

Does anyone if there are any original paper(s) that first introduced the notion of group action or permutation representation, and who the author(s) were? Any references I have found so far on e.g. ...
103 views

### Relation-preserving maps as morphisms of a category

What is the canonical name for the category whose objects are all pairs $(X, \rho)$, where $X$ is a set and $\rho$ is a binary relation on $X$, and whose objects are relation-preserving maps? That is, ...
176 views

### Weak Partial Complete Lattice and Homomorphisms

What is the proper nomenclature for a generalization of a lattice $L$ such that not all subsets of $L$ may have a join/meet, sometimes not even for finite subsets? This paper calls it a "weak partial ...
131 views

### Textbook determinant convention

My text book is called "Linear Algebra and its applications" by David C. Lay. I am just wondering why the textbook uses the absolute value symbol when it wants us to compute determinants. For ...
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### Resources to learn the meaning of any math symbol

There is lots of symbols and may be operators like || in this expression $$3^k||n$$ that I would like to be able to quickly find the meaning of. I tried Wolfram|Alpha but I think it expects the ...
115 views

### What letter should I use to denote an ideal?

In commutative algebra, there seem to be two rather different notational conventions for ideals: either $I,J, \dots$ or $\mathfrak{a}, \mathfrak{b}, \dots$. By itself, it is hardly surprising - after ...
210 views

### History of Lie algebra notation (in Fraktur)?

Does anyone know how it has become the standard to express Lie algebras in fraktur? I'd also like to know how it's established for each era and region, not only the origin. It doesn't seem that ...
547 views

### Notation to work with vector-valued differential forms

What it the standard notation used while working with vector-valued differential forms? I tried using abstract index notation, for example denoting a $1$-form valued $2$-form as $P_{i[bc]}$, but I'm ...
688 views

### Mathematical notation for computer science

Can anyone point me in the direction of good introductory material on the use of mathematical notation in the field of computer science? I often come across notation in research papers that I don't ...
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### Articles on ideas in the history of mathematics notation?

I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
I've always wondered why finitely generated modules are of form $$M=Ra_1+\dots+Ra_n$$ while finitely generated algebras have form $$R=k[a_1,\dots, a_n]$$ and finite algebras have form ...
Previously, I have seen matrix notation of the form $T_{ij}$ and all the indices have been in the form of subscripts, such that $T_{ij}x_j$ implies contraction over $j$. However, recently I saw ...