# Questions tagged [terminology]

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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### Where can I get a formal definition of "branching points"? [closed]

I'm taking my complex analysis course, and I would like to know if somebody can please give me some advice on where can I find the definition of "branching points".
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### Can't parse a statement in an article on coalgebras and umbral calculus

I am reading Nigel Ray's "Universal Constructions in Umbral Calculus" (1998, published in "Mathematical Essays in Honor of Gian-Carlo Rota", page 344). The article reads: We ...
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### What is the meaning of logarithmic density in layman's terms?

The way that I understand natural density is that it is an "intuitive way of describing the size of a set", whereas cardinality is an "absolute way of describing the size of a set"....
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### What does "almost all in the sense of logarithmic density" mean in Tao's Collatz paper?

Tao's paper: "Almost all orbits of the Collatz map attain almost bounded values" (via arXiv.org) 1st related question/discussion, I did not understand: Meaning of "almost all" in ...
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### When mathematicians say "true" do they mean "true in all models"?

According to the comments to this question, Truth is ordinarily defined by reference to models. If so, even axioms and theorems are not true without reference to a model. However, when ...
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### what math concept would this be called?

Assume that I am trying to use reference values to evaluate an analysis of an unknown sample in order to determine what the nature of the sample is and the attribute value is an 8-bit string of binary ...
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### What is the opposite of antiparallel?

Is parallel really the opposite of anti-parallel? While anti-parallel indicates that two vectors are directed along the same line and are pointing in opposite directions then it seems to me that ...
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### Is there a name for this vector space?

I've seen in some books of Analysis the notation $\mathcal{L}(\mathcal{L}(V), V) \cong \mathcal{L}_2(V)$ and I don't find anything about this vector space. What is it? Is there a name for it? Also, if ...
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### terminology needed regarding convex bodies

Let $K$ be a convex body in $\mathbb{R}^n$. I'm looking for a term for a continuous function $f: \mathbb{R}^n \to \mathbb{R}$ that is zero on $\partial K$, negative on the interior of $K$, and ...
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### Does $(p\implies q)\implies\neg( q\implies p)$? [closed]

$p\implies q$ does not necessarily indicate that $q\implies p$, which is why there exists a double-sided implication: $\iff$. $p\iff q$ is the same as saying $(p\implies q)\land(q\implies p)$. However,...
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### 4 elements are named x,y,z,w now how to name 8 elements [closed]

I have a vector of four elements. The elements are named x, y, z, w: Vec4(x, y, z, w) Now I have another vector of eight ...
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### How to formally define this square matrix?

I was wondering if there is formal name for a 3x3 matrix where the third column is the sum of the first two columns and the third row is the sum of the first two rows. In other words, a square matrix ...
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### Term for a product of groups that is neither direct, nor semi-direct, but generalises semi-direct ones

Suppose $H$ and $K$ are subgroups of a group $G$ such that every element $g\in G$ can be uniquely written as $g = hk$ with $h\in H$ and $k\in K$. (It follows then that every element $g\in G$ can also ...
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### What are $0$ and $1$, the elements of $\mathbb Z/2\mathbb Z$? How do they relate to $\mathbb Z$? [duplicate]

I often see field $\mathbf{Z}/\mathbf{2Z}=\{0,1\}$. Without other indication we might see elements of field $\mathbf{Z}/\mathbf{2Z}$ as a subset of $\mathbf{Z}$. Operations such as $2+1=3=1$ are also ...
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### Name for an almost diagonal real matrix

If $A$ is a real square matrix which is diagonalisable over the complex numbers, then it is conjugate (over the reals) with a matrix $D$ which is block-diagonal, where each block on the diagonal is ...
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### Why does “propositional calculus” have the word “calculus” in it?

We define “calculus” like this: “Calculus is the mathematical study of continuous change.” But if that’s the case, then why is the study of (true or false) propositions and their relations called: “...
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### What is the name of the logical equivalence $p\land\neg p\equiv\bot$?

The conjunction of any statement $p$ by its negation is a contradiction. That is: $$p\land\neg p\equiv\bot$$ Do you know if there is a name for this logical equivalence?
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### What category is this? (Objects are sets and distinguished subsets of power set)

Let $\mathcal{C}$ be the category whose objects are sets $X$ equipped with distinguished subsets of the associated power set $\mathcal{U}_X \subset \mathcal{P}(X)$, so that their union is all of $X$ (...
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### (Terminology) Name for a subset that has non-empty intersection with every block of a partition?

Consider the following data: a set $X$, a partition $\mathcal{P} := \{B_i\}_{i \in I}$ of $X$ whose elements $B_i \subseteq X$ are called "blocks", and another subset $Y \subseteq X$. ...
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### Meaning of "on" in the expression "operation on a set $A$"

What is the meaning of "on" in the expression "operation on a set $A$"? Does it mean that: at least one of the operands is in $A$; all the operands are in $A$; or all the operands ...
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