# 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 difference between $(f^{-1})^{-1}(A)$ and $f(f^{-1}(f(A)))$?

I asked a question Under what condition does $f(f^{-1}(f(A))) = f(A)$? and it totally backfired because people were confused whether $f^{-1}$ is the preimage or the inverse function Let $f: X \to Y$ ...
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### Notation of a function that Maps two sets into a Matrix

Given two sets $P, V$ a function $f(t)$ takes any element that belongs to $P$ or $V$ e.g. $t \in P \cup V$ returns a matrix of $2$ columns and $K$ rows. What is the proper notation to express ...
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### Converting from standard to functional, Polish and Reverse Polish notation

I wanted to convert the following expression to Functional, Polish and Reverse Polish notation. $$Y =A + \frac{B+ \dfrac{BA}{B+CA}}{A - \dfrac{BC}{B-C+A}}$$ I know how to do Standard -> Functional ->...
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### Are integers relevant for every Group?

The definition of the order of an element in a group is: The order of an element $x$ of a group $G$ is the smallest positive integer $n$ such that $x^{n}=e$. Doesn't this definition assume that ...
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### What is $\circeq$ used for?

I was looking for a way to put 'des' over the equals sign in latex and stumbled upon this symbol $\circeq$ What are mathematicians using it for?
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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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