# Tagged Questions

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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### 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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### 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 ...
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### 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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### 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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### $\nabla ^2 G$ 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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### 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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### 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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### 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: $$\sum_{i>j}$$ ...
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### 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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### 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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### 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 ...
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### 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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### 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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### 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?