Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.

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33 views

What is the symbol that is used for the universal set in these two textbooks? [closed]

From this textbook: And this textbook: It looks like a squiggly E (\mathcal{E}) or perhaps it is the Greek letter xi (ξ). But I am not sure.
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1answer
18 views

A question about convention of writing identities and formulas

I'm only a third year undergraduate math student, but I've seen a decent amount of formulas, identities, and equations (at least enough to formulate such a question). However, I haven't actually ...
1
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1answer
25 views

Symmetric Simple Random Walk - Definition Clarification

I'm finding conflicting answers everywhere, including in my own notes. In the phrase "symmetric simple random walk", which part, "symmetric" or "simple" refers to having a probability of $0.5$ to go ...
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2answers
28 views

Notation for sets that do not overlap

Is there notation to describe, say a set that consists entirely of two mutually exclusive subsets? Say $ D = D_1 \cup D_2 $, how to indicate that $D_1$ and $D_2$ do not overlap?
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0answers
56 views

Is it okay to say $\cos(a)$ where $a$ is a vector?

Assume you have vectors $a$ and $b$. They are not precisely defined but in the text mentioned as vectors. Can I use the following notation to mean element-wise product of $a_k$ and $\cos(b_k)$? ...
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2answers
44 views

Should I write $x (f(x))^{-1}$ with less parenthesis.

In this case, $x$ and $f(x)$ belong to a multiplicative group. I would like to write $x f(x)^{-1}$ instead of $x(f(x))^{-1}$. I figured that I could explain once what I mean by $x f(x)^{-1}$ and then ...
6
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4answers
128 views

Why is $\cos(x)^2$ written as $\cos^2(x)$?

I'm just wondering why the square of $\cos(x)$ (i.e.: $(\cos(x))*(\cos(x))$) is almost universally written in the form $\cos^2(x)$ rather than $\cos(x)^2$. This seems particularly bizarre when one ...
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2answers
122 views

What will mathematicians do when they run out of letters in the Greek and English alphabets? [closed]

Like x,y,z are commonly understood to be dimensions and theta is an angle and Pi is a specific irrational constant, and Tau is half of Pi, etc. etc. etc. They must be running out of letters by now. ...
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4answers
71 views

Why do univariate indefinite integrals carry the $\mathrm {d}x$?

I understand that the $\mathrm {d}x$ sort of comes from the $(x_i-x_{i-1})$ term in the Riemann sums of the integrals (just like the $\mathrm dg$ for Riemann-Stieltjes integrals), but when working ...
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votes
1answer
46 views

Is “the reals” a slang term for $\mathbb{R}^d$ where $d = 1$?

Often times I see people referring to certain functions as a mapping from $\mathbb{R}^d$ to "the reals", are they referring to $\mathbb{R}^d$ where $d = 1$? Sorry for the potentially trivial ...
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1answer
21 views

Einstein Summation Convention Minkowski Metric

Picked up a book on General Relativity for Mathematicians, but I'm a bit unclear on some of the tensor notation. For example, the Minkowski Metric $$\eta_{\mu \nu} (\Delta x^\mu)(\Delta x^\nu)$$ ...
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2answers
50 views

Integrals without terms possible?

Is an integral without a term possible? I don't know the specific name for the term at the end but here is an example: $\int x $ vs $\int$$ (x) dx$ And does $\int$$ ((x) dx) \Rightarrow ...
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4answers
561 views

Is Sigma $\Sigma$ a mathematical way of doing a for loop?

I've been a programmer for ten years, and once upon a time I was pretty good at math. Those days are long gone. I'm taking some online classes and now I find myself needing to remember the math I ...
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0answers
12 views

Notation for “vectorized” function

Is there a notation for expressing vectorization of a function as implemented by Mathematica's Map ...
1
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1answer
33 views

Is interval a set?

Given a function $f$; $$ f(x) = \frac{x}{1+x^2} $$ the support of $f$ is $$ \mbox{supp}f=\begin{cases} \overline{\{(-\infty, 0), (0, \infty)\}}=(-\infty, \infty)=\mathbb{R}&&(1)\\ ...
2
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2answers
114 views

How to write this statement in mathematical notation?

No integer bigger than 70 can be expressed as a sum of 3 integers smaller than 30 My attempt: $U_1 = {x∈Z∶x>70 }$ $U_2 = {y∈Z∶y<30 }$ $∄x ∈ U_1 , ∀y ∈ U_2 , x = y_1+y_2+y_3$ I understand that ...
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1answer
18 views

Why aren't the degrees of freedom included in the confidence interval formula?

I have one question. In the formula for calculating the confidence interval, I don't see the degrees of freedom in the formula. In my book, the formula is : $$\text{Confidence interval:} \qquad \mu ...
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1answer
22 views

If $f:\mathbb{R}^2\to X$, how do we call $f_{x_0}(y) =f(x_0,y)$ as a function of one variable?

For obvious reasons coming from probability theory I have been calling the function $f_{x_0}(y)$ ($x_0$ fixed) "marginal function". However, reviewing some literature I've noticed that the word ...
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0answers
35 views

What happens when an element of a set is used in a rule but doesn't exist for certain n?

Suppose we have the set: $\{I_1,\dots,I_n \mid l_{j+1} < r_j < l_{j+2}\} $ where $I_j = \{l_j,r_j\}$ for $n \geq 2 $ Here we have a set of intervals, with left and right values of the ...
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1answer
18 views

What does $c_1(a,b)$ mean in the context of a solution to a PDE?

The solution to the PDE $$u=r\cdot\nabla u= x\, \partial_xu + y\,\partial_yu + z\, \partial_zu$$ where $u=u(x,y,z)$ is given by Wolfram Alpha as ...
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5answers
102 views

What does $\ln(\ln(x))$ simplify to?

What does $\ln(\ln(x))$ simplify to? First instinct was to write $\ln^2x$, but that looked odd, because $\ln(\ln(x))$ is not the same as $\ln(x)\ln(x)$ or $(\ln(x))^2$. Or is it ?
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0answers
31 views

Why are Sobolev spaces $W^{m,p}$ denoted with the letter “W”?

Why are the Sobolev spaces $W^{m,p}$ where $m\in\mathbb{Z}$ and $p\in\mathbb{Z}$ with $1\le p\le \infty$ denoted with the letter "$W$"? I know they are denoted with the letter $H$ when $p=2$ because, ...
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1answer
27 views

Common notation for non vacuous implication

Taking the definition of vacuous truth to be an implication where nothing satisfies the antecedent. Is there notation commonly used for "non-vacuous implication"? I could write: $(\forall x . P(x) ...
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1answer
38 views

Notation (manifolds, harmonic analysis)

I was reading the paper "On the Multilinear Restriction and Kakeya conjectures" by Bennett, Carbery and Tao For each $1\leq j\leq n$ let $U_j$ be a compact neighborhood of the origin in ...
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2answers
48 views

$\nabla ^2 G$ meaning

If $G$ is a function with three components. $G$ is actually a Green's function in my case, like $G( \textbf{x} , \xi)$ with $\textbf{x} = (x,y)$ and $\xi = (\xi _x, \xi _y)$ so I am guessing it is ...
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2answers
39 views

What is the $\setminus \{a\}$ in $x \in [ a - \delta, a + \delta ]\setminus \{a\}$?

What does the $\setminus \{a\}$ in $$x \in [ a - \delta, a + \delta ]\setminus \{a\}$$ mean?
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2answers
70 views

An example for a mathematical object that has two indexes, and is not a tensor

I understand how to check if something is a tensor (if it transforms like a tensor, it's a tensor). I have this example of a rank 2 tensor: $$\tau_{ij}=r_if_j - r_jf_i$$ and I understand that it is a ...
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1answer
14 views

Notation $\dot{=}$ Amann's book Linear and quasilinear Parabolic Problems

Do someone knows this notation $\dot{=}$? I'm studying Amann's book and he uses this notation but I couldn't find a definition in his book. For example, he writes $$E_1\cap E_0\dot{=}E_1\ and \ ...
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2answers
58 views

How to write a sum that only includes even terms?

Suppose I have a sum $$\sum_{n=0}^{\infty}f(n)$$ and that for $n$ even $f(n)\neq0$ but for $n$ odd $f(n)=0$ how could I write the sum to indicate that only the even terms need to be summed. I have ...
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1answer
39 views

I know what a Complex Plane is, but what is a complex $k$-plane?

This may be somewhat related to physics, but I saw in a non-English paper (which I googled "complex $k$-plane" for some constant real $k$) that mentioned a complex $k$-plane. $k$ in its context was ...
0
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1answer
15 views

Function with with consecutive brackets

What is the meaning of a function like: $f(x)(y)$ It seems to me that this is another way to express the composition of function $f$ with function $x$. Am I right? But then why don't just use the ...
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0answers
24 views

How to notate the evaluation of a multivariate function with given values?

As the accepted answer in this question makes clear, the vertical pipe with a single number at the bottom makes it easy to notate the value of a univariate function at a specific point, like so: ...
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2answers
114 views

What is a good notation for an “even falling factorial”?

It has been suggested to me that I use this notation: $$ \lfloor n \rfloor_2 = 2 \left\lfloor \frac n 2 \right\rfloor = \text{“even floor of $n$''} = \text{largest even integer}\le n. $$ I also want ...
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0answers
32 views

Notation of a point on a plane

I'm having trouble finding the correct way to notate following conclusion about plane $H$ and point $A$. ($A \in H$) If plane $H$ is not parallel to the $yz$-plane of the coordinate system, a ...
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0answers
41 views

A more shorter way of writing $[X-d, X+d]$?

Confidence intervals are usually of the form $[X-d, X+d]$, where $X$ and $d$ are repeated twice. Is there a more compact way of writing this?
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0answers
10 views

How to interpret this index variable and corresponding summation limits?

Let $TD$ be an integer (That is, $TD \in \{ 1,2,3,4,\dots \}$). I am looking at the following statement: If $TD$ is even, the (solution) is given by $$ \forall \frac{TD}{2}\in \mathbb{N}: x_i^* = 1 - ...
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3answers
84 views

Notation: What does $\sum_{i>j}$ mean?

I'm currently writing a review of neutrino oscillation however there is one line that I don't understand: More specifically, I do not understand the condition on the summation: $$\sum_{i>j}$$ ...
0
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1answer
37 views

Notation for double-integrals - partial or full differentials?

When you are trying to find a volume for a function z = f(x,y), the common notation is to find: $$\int\biggr(\int f(x,y)dx\biggr)dy$$ However, when you do this, you are actually keeping the $y$ ...
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1answer
24 views

What does this notation, used in Markov Chains, mean?

In my module on Markov processes, the following notation is used: $$ p_{ij}^{(m,n)} = P(X_n = j \mid X_m = i) \quad \text{where } \: m<n \\ p_j^{(n)} = P(X_n = j) \\ p_{ij}^{(k)} = \: ??? $$ Does ...
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2answers
56 views

Verbal Explanation of Math Notation

I am looking at a definition for an induced subgraph. I completely understand what an induced subgraph is, so an explanation of that is beside the point. What I am really interested in is a ...
0
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1answer
25 views

Problem on defining tuple notation that includes a set

I'm struggling with preparing a notation for a project im working on that includes the following: I have a tuple $s_i$ that is currently described by a timestamp and a value like this $(t_i, v_i)$ ...
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0answers
31 views

Functions acting on the right

My question is with regards to correct notation when a function "acts on the right". In the following $A, S \neq \emptyset$, $A^{*}$ denotes the free monoid on $A$ and Map$(S, S)$ all maps with domain ...
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4answers
75 views

What is the meaning of the notation $x \in 2^{\mathbb{R}^n}$?

In a paper [that is to be published], I encountered following notation: $x\in2^{\mathbb{R}^n}$ What does this mean?
0
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1answer
26 views

Big Omega/Oh Notation (Application)

For clarity; I use the following definitions (taken from Wikipedia), in my question: Big Omicron: $f(n)=O(g(n))$. Formal definition: $\exists k >0,\exists n_{0}, \forall n>n_{0}: |f(n)| \leq k ...
3
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0answers
49 views

what does the bar means for an integer?

It's in arithmetic context (not complex), and it's an integer (no decimal point). The question was to find the answer of the product of 2 numbers $\overline{323}^6$ and $\overline{35}^6$, both in base ...
38
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9answers
5k views

Correct set notation for “all integers which are not multiples of 7”?

What is correct set notation for "all integers which are not multiples of $7$"? My best guess is: $$ \{ x : (\forall k \in \mathbb{Z})(\neg(7k = x)) \}$$ Or $$ \{ x : \neg(\exists k \in ...
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0answers
37 views

What does the broken vertical bar ¦ mean?

I have a question which I am unable to solve because I don't know what the broken vertical bar ¦ stands for: If $\mathbf a\cdot \mathbf b = \mathbf a\cdot \mathbf c$ where $\mathbf a ¦ \mathbf ...
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0answers
12 views

Problems in notations in a paper on Bayesian space-time models

Suppose I have been given some process $Y$. Let $Y(s,t)$ denote the value of process at location $s$ and time $t$. For my experiment, I consider a model described as - $$Y(s,t) = \mu(s) + ...
21
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5answers
1k views

Why do we say function “parameterized by” vs just function of (x,y,z,…)?

I'm studying statistics, and in a lot of textbooks, the regression formulas always refers to the functions themselves as f(x) parameterized by a,b,c or something. And they are often written $f(x; ...
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1answer
25 views

Mathematical notation for a value increase until a certain limit is reached

How can I say, using mathematical symbols, "x increases until a certain limit is reached"? To give a bit of background info, what I am trying to say is that pressure (x) increases in a pipeline ...