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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Definition of error while computing order of convergence

I'm trying to verify order of convergence for implicit Euler method. Theory suggests that it should be $O(\Delta t + \Delta x^2) .$ We know the formula for order of convergence : $$\rho = \frac{log(...
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A discrete probability distribution, but the population is continuous vs. discrete

Suppose we have some sort of discrete distribution as follows: fruit frequency apple 0.3 orange 0.5 tomato 0.2 This is a statistical description of the actual population, which is ...
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Is there a name for this iterative procedure for estimating a parameter using MSE?

Suppose $X_1, \cdots X_n$ are $\mathcal{N}(A, \sigma^2)$ random variables, with some unknown mean $A$. Let $\hat{A} = \frac{1}{n}\sum_{i=1}^{n}X_n$ be their sample mean, and let $a$ be some real ...
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Why is a vector bundle called E?

Vector bundles are often denoted as $p:E \to B$, where $p$ is a projection map, $B$ is the base space and $E$ is the total space. Here the choice of the letters $p$ and $B$ is clear, but is there also ...
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What is the origin of the (V)BODMAS rule?

When finding out the origin of the (V)BODMAS rule, found out this from google "BODMAS was introduced by Achilles Reselfelt to help in solving mathematical problem involving operational signs. ...
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Name for class of functions from Øksendal's Introduction to SDEs

From Øksendal's Introduction to Stochastic Differential Equations we have the following: Definition $3.1.4.$ Let $\mathcal{V} = \mathcal{V}(S, T)$ be the class of functions $f(t, ω): [0, ∞) × Ω → R$ ...
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What is the name for the maximum power of a variable in the terms of a multivariable polynomial?

Consider a multivariable polynomial, for example, $f(x, y, z) = 1 + 2x + 3xy + 5zy + 3xy^2z + 2x^2y$. The degree of this polynomial is $4$ because of the $x y^2z$ term. I am looking for the name for ...
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On terminology; what is meaning of the “decrement” of a permuation? (or what is the alternative word or phrase used for this definition)

In a Russian text, on the topic of Permutation Groups, the author introduces the concept of the decrement of a permutation defined as follows: (Note that this is my translation of the text, so it ...
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84 views

Correct Terminology in the Context of Rings

Suppose I have a ring $(A, ◦, •)$ where $A$ is a set of elements $\{α, β, γ,\ldots\}$. Can $◦$ and $•$ with which the ring is equipped be properly termed, in English, its "internal laws of ...
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What's geometric about a “geometric progression”?

An arithmetic progression is $a+0b, a+1b, a+2b, ..., a+nb$ A geometric progression is $ab^0, ab^1, ab^2, ..., ab^n$. Multiplication is arithmetic, so why is a geometric progression not also an "...
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History: Direct Product became Tensor Product?

A question perhaps for the older members of the stackexchange community ..... I'm reading a 1939 paper by the great and famous J. von Neumann, "On infinite direct products" (of vector spaces)...
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Find the relationship between $x$ and $y$ so that $y:=0\rightarrow\frac{\pi}{2}\Leftrightarrow x:=y\rightarrow\frac{\pi}{2}.$

Find the relationship between $x$ and $y$ so that $y:=0\rightarrow \dfrac{\pi}{2}\Leftrightarrow x:=y\rightarrow \dfrac{\pi}{2}.$ I'm having trouble solving the multivariable calculus if I change the ...
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why is the “not” operator considered an operator

an assertion as i understand it is, a claim. so, something like "i like jello". It can be false or true. The "not" operator switches the boolean value of a statement. so if ...
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Is there a name for “point to set distance” when you vary the distance?

Recall: let $X$ be a metric space with metric $d$. Let $x\in X$ and let $A$ be a subset of $X$ and define $$d(x,A)=\inf\{d(x,a)\mid a\in A\}.$$ This $d$ on the LHS is called a just point-to-set ...
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Is $n = 0$ in proofs involving mathematical induction a rigorous expression?

I have had this confusion from high school. In proofs involving mathematical induction, we always say for $n = 0$, blablabla, so that a certain condition holds for $n = 0$. After I learned logic, I ...
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Number of balls touching one ball at the center.

Let $B$ be a ball of radius one in $\mathbb{R}^d$. I'm looking for references about the following problem : How many disjoint balls $B_i$ of radius one is it possible to put in contact (tangential ...
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What is the difference between an indeterminate and variable?

From Wikipedia- In mathematics, and particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else but itself and is used as a ...
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A problem related to minimizing the multiplication signs

Let me introduce you some (maybe) new things i.e., $$a^{2}+ b^{2}+ c^{2}- ab- bc- ca:=\left ( c- a \right )^{2}- \left ( a- b \right )\left ( b- c \right )$$ $$b^{2}- 4ac:=\left ( c- a \right )^{2}- \...
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Why does an infinite limit not exist?

I read in Stewart "single variable calculus" page 83 that the limit $$\lim_{x\to 0}{1/x^2}$$ does not exist. How precise is this statement knowing that this limit is $\infty$?. I thought saying the ...
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What is the term for simple (non-matrix) math?

Is there a term for "simple" arithmetic where all variables in the expression contain only single/scalar values and thus produce a scalar result? This is opposed to matrix math where a ...
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Why are some functions called 'forms'?

The question is simple: why are some functions called 'forms'? Modular 'forms', bilinear 'forms', differential 'forms', quadratic 'forms', and so forth. It is not concretely a mathematical question ...
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1answer
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Term for repeated exponentiation?

Is there a term (or operation) for repeated exponentiation? I.e. Repeated addition is multiplication, repeated multiplication is exponentiation, repeated exponentiation is X? Is there even such a term ...
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Name of a certain set of vectors

Let $v,u\in V$, a normed vector space (or I guess a normed magma if we want to be general), and let $l=(l_1,\dots,l_n)$ be a list of positive lengths. Then what do you call the set of "chains&...
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Is there a name for function $f(x)=\max(a, \min(x, b))$, where $a \leq b$?

Is there a name for function $f(x)=\max(a, \min(x, b))$, where $a \leq b$? What actually this function does: it keeps value in bounds of $[a, b]$.
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Representation theory: terminology

I am learning about representation theory. One of the things which continually trips me up is the (abuse of?) notation $V$ for a representation. Normally, one writes $(\rho, V)$ for a representation, ...
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Property of $f(x, y)= z$ for all permutations of $x, y, z$

What property would you say a function $f(x, y)= z$ has if it is true for all permutations of values $x, y, z$?
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Is the length of a line a property of that line, or is it its own mathematical object?

I'm trying to understand the nature of mathematical objects. As far as I understand it, mathematics studies these objects. Geometric shapes are one kind of such object, including 1D shapes, namely ...
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Confusions with Symbol “=” in Mathematics

I am having this question because of the axiom of equality: \begin{equation} \forall x \forall y \left(x = y \longrightarrow \forall z\left(z \in x \longleftrightarrow z \in y\right)\right). \end{...
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Ideal of a group

The ideal is defined in the ring theory; In ring theory, a branch of abstract algebra, an ideal of a ring is a special subset of its elements In the answer to this question What is the exponent of a ...
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Does a mathematical definition have necessary and sufficient condition hidden in it? [duplicate]

Let us assume the following definition: `` S is said to be A if S satisfies the condition C. '' -----------(P) Can it mean that: `` S is A if and only if S satisfies the condition C. '' ---------- (...
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Probability distribution vs. probability mass function (PMF): what is the difference between the terms?

Consider a discrete case. PMF is the probability each value of random variable gets. So, for example, X ~ Poisson(2). I plot these probabilities (below), so I can say that I show the PMF of X. But on ...
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Confusion on the definition of an indexed family of sets

Ive recently been learning set theory and a bit of topology and im very confused on the definition of an indexed family. Why do we say a family of sets instead of a collection of sets? And why is the ...
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Question on terminology for implications when consequent is always true.

The implication $X\rightarrow Y$ is referred to as being vacuously true when the antecedent is false (i.e., $X=\bot$). Is there similar terminology to be said when the consequent is true (i.e., $Y=\...
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Is $\sqrt[3]{x^3}$ monomial? [duplicate]

I have been confused by different interpretations of polynomial and monomial. Is $\sqrt[3]{x^3}$ really a monomial?
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Using “implies” to refer to material conditional

Is it acceptable to translate the binary connective "$\let\ f\rightarrow$" into English with "implies"? I'm unsure because "implies" for me immediately brings to mind logical implication, but I've ...
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Is there a common name for the shape described as a segment of a circle or ellipse?

A circular segment is a region of the area inside a circle partitioned from the rest of the circular area by a chord. Is there a common name for this shape, other than "circular segment"? If ...
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A standard name for an “inversely (uniformly) continuous” map

Is there a standard name for a map $f: X → Y$ between metric spaces such that for every $ε > 0$ there is $δ > 0$ such that $d(x, y) < δ$ if $d(f(x), f(y)) < ε$ for $x, y ∈ X$ and/or for a ...
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Symmetric vs Symmetrical

I was reading an engineering book. It says " A turbomachine with symmetrical velocity triangles...". I personally felt more naturally right away to say symmetric velocity triangles. What is ...
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44 views

Composite vs Composition: which one is the correct word?

So, I am a bit confused about the word I should use to refer to $$f\circ g.$$ I have always used ''composition'' but I have seen some people (perhaps everyone who uses the term correctly) say ...
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What is meaning of term “ F is Algebraic Galois over K”

I am trying exercise questions in Field Theory from Algebra by thomas hungerford and there in some questions author asks about prove that " F is algebraic Galois over K". Now, I am not able ...
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sine vs Sine: understanding the differences

I was using the textbook A History in Mathematics by Victor J. Katz. I saw a theorem from Nasir al-Din al-Tusi. The way the theorem is written in the book is like this: In any plane triangle, the ...
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What is the difference between counting and measuring?

Are counting and measurement the same thing? I think that they are different since in my mind the idea of counting pertains to discrete objects while the idea of measurement pertains to continuous ...
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Are pairwise mutually exclusive events the same as mutually exclusive events?

Larson (1982) defining the probability axioms talks about "mutually exclusive" events, while Poirier (1995) about "$A_1, A_2, \ldots$ as a sequence of pairwise mutually exclusive events events in the ...
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$k$th-order Taylor polynomials rules in English / US math education

In France, an important topic for undergraduates in analysis is what is called Développements limités. The concept is based on $k$th-order Taylor polynomials. It uses a series of rules like: The $k$...
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all but finitely many terms

So I found a definition in my notes for a sequence to be convergent. It said that a sequence is said to converge to a real number $L$ if every open interval containing $L$ contains all but finitely ...
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What is the difference between a partition and a subinterval? [closed]

For example the norm of a partition is the widest subinterval
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How to understand the convention on describing the “position” of mathematical objects

When studying algebra, I find that it seems like a convention that we use positional words like on, under, over etc. to describe relations between things. For example: $V$ is a vector space over $F$. ...
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Understanding Slope Better

Recently, I have realized how much I have taken for granted in understanding the slope of a line and the slope of a curve in general. With that said, I wanted to clear up my understanding to make sure ...
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How do constants differ from numbers?

Although I scanned the other version that's not Early Transcendentals, in Calculus Early Transcendentals 7th ed 2011, James Stewart never defines "constant". It first appears on p. 3 but not ...
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Is there an accepted term for the opposite of mode in statistics?

In descriptive statistics, there are terms for all sorts of things. The mean, median, and mode for a set of data are each three very frequently thrown around examples. The mode in particular is ...

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