# 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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### Translating between Set Theoretic and Interval notation

Given an open interval (or closed it makes little difference to the question) on the Real Field $(a, b)$, where $a,b$ are real numbers, and an arbitrary predicate $P(x)$, which is true for all ...
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### Is there a notation for space of all random variables?

Is there a common notation for the set of all random variables of the form $X:\Omega\to\mathbb K$? I'd like to use it as a shorthand when i need to specify, e.g., that some function actually maps ...
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### Total derivative using $(x,y)\mapsto f(x,y)$ notation

Related to What is the difference between $\frac{\mathrm{d}}{\mathrm{d}x}$ and $\frac{\partial}{\partial x}$? Is it possible to make sense of $(x,y)\mapsto f(x,y)$ when taking the total derivative ...
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### What is the proper notation for vectors that uses only integers? $\Bbb Z^n$?

How do I denote vectors, similar to $\Bbb R^n$ but with integers instead of the reals? Just $\Bbb Z^n$? Would vectors of exclusively positive integers be $\Bbb Z^{{+n}}$ then? (since $\Bbb Z^+$)
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### Math notation to show two numbers in a range that added together get the max of the range [closed]

I am completely new to math notations, it's been about 30 years since high school, and I am writing a research paper (completely on my own, not for a degree). I basically want to show that two real ...
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### The $n=0$ term in the power series $\sum_{n=0}^\infty a_n x^n$

This question is about the definition and notation for the $0^{th}$ term of the power series: $$\sum_{n=0}^{\infty} a_n x^n$$ There are two possible ways to interpret this term: 1) It is just a ...
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### Notation: rotation matrix with a condition

I'm building a space simulation & am using this resource for converting Keplerian Orbit Elements to Cartesian Co-ordinates. The notation for step 6 has me slightly confused: Is the top part ...
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### is Cov(X) and Var(X) same? when X is random vector

i'm studying with hogg. introduction to mathematical statistics. and i learned about random vector but i wonder whether Cov(X) and Var(X) is same or not. as intuitive thinking , if X is a random ...
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### Index notation in vector functions

Suppose I have a vector $\vec u$ that depends on a vector $\vec x$ and a scalar t, so each component of $\vec u$ depend on all components of $\vec x$. How can I show this relationship with index ...
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### Notation for the subset of a set without the last elements

I have an ordered set $S=\{23,45,32,56\}$ I would like to make an ordered subset $M=\{23,45,32\}$ which contains the elements of $S$ except the last one. In this case. How do I represent this formally ...
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### ordered set notation in functions

Do please forgive me, if this question is a duplicate. How does one correctly notate a function $f$, which takes a ordered subset $S$ from the field $\mathbb{K}$ and returns an other (ordered) subset ...
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### Asymptotic notation basics

Say that we have the function $$f(n)=kn, \, k>0$$ does that imply the following? $$f(n) \in O(n), \, f(n) \in \Theta(n) \text{ and } f(n) \in \Omega(n)$$ I'm fairly new to these notations and am ...
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### What does $(0:x)$ mean?

The following excerpt is from Eisenbud's "Commutative Algebra with a view toward Algebraic Geometry" on pg. 424 We can decide whether an element $x\in R$ is a nonzerodivisor from the homology of ...
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### Question on the Notation of an Abstract Algebra Question

The following is a question that I came across in a textbook I'm reviewing for self-study. The book is "Introduction to Abstract Algebra", 4th Edition, by W. Keith Nicholson. I have a question both ...
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### What does the middle dot in parentheses mean?

The below picture is from section 3.3.1 in this paper; I'm not familiar with the notation of using middle dots in square parenthesis. Are the authors using this simply to indicate that any two ...