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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Is there any notation to denote the solution of a particular equation?

Let's say that I have an equation: $$x + 2 = 7 + y$$ If I need the solution for $x$, I can solve it and then use $5 + y$. No problem there. But say I have an abstract equation. For now I am ...
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Convention on Cauchy's two line notation for permutations

Let $n\in\mathbb{N}$. A permutation $\sigma\in S_n$ is denoted in Cauchy's two line notation as follow: \begin{pmatrix} 1 & 2 & \cdots & n \\ \sigma(1) & \sigma(2) & \cdots & \...
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What does the $(m,n)$ mean in context of $\mathbb{Z}_{(m,n)}$

On the section about the Hom sets of modules, Hungerford has an exercise that asks to show that $$\operatorname{Hom}(\mathbb{Z}_m, \mathbb{Z}_n) \cong \mathbb{Z}_{(m,n)}$$ and then in the next ...
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How to describe a summation of $\frac{1}{2^x3^y}$ and evaluate.

I want too calculate the value of this sum: $$\sum \frac{1}{2^x3^y}$$ Where we sum up all permutations of terms involving a nonnegative integer $x$ and a nonnegative integer $y$. How can I ...
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Definition of function

When defining a function, mathematicians often write something like this: Let $f\colon \mathbb R\to \mathbb R$ be the function given by $x\mapsto x^2$. The purpose of this definition may be to ...
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About the notation of composition of permutations in Lang's book

In Lang's "Algebra", p.30-31, I'm confused about the order of reading the composition of two permutations. In p.30, it seems that we read it from left to right (see the bottom equations), but for p.31,...
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Does the Statement $\lim_{f(x)\to a}k(x)$ Make Sense

In a formal mathematics context does the statement $$\lim_{f(x)\to a}k(x)$$ where $f(x)\neq c$, where $c$ is a constant, make sense? For example does $$\lim_{x^2\to 0}x$$ make any sense in a formal ...
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Notation check, argmax of values in a set [on hold]

Among C different possible values for each y and m total ...
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Unclear passages in the paper “On a New Class of Theorems in Elimination Between Quadratic Functions” by J. J. Sylvester

I'm writing an essay about the origin of some mathematical terms in the work of J. J. Sylvester. He first used the word matrix in his paper Aditions to the Articles "On a New Class of Theorems" and "...
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Simple set-builder notation for counting pairs

Today I was curious about writing a simple expression using set-builder notation. The expression is the number of integer pairs $(a, b)$ such that $a \mid n$, $b \mid n$, and $a \mid b$. My attempt is ...
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How do I write $B = \left\{\left[\begin{smallmatrix} x \\ y \end{smallmatrix}\right] \in \boxed{?}| \ldots\right\}$ with proper notation

Let $x \in X \subset \mathbb{R}^n$, then I define a set: $$A = \{x \in X| 1^Tx = 0\}$$ Now supose I have another element $y \in Y \subset \mathbb{R}^n_{+}$ I concatenate $x,y$ in to a single vector ...
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Double integral, $dx$ before the integral sign

Suppose we have $f(x)g(x,y)$, In some books (Rudin Real and Complex Analysis) the double integral is written as $$\int_X f(x) dx \int_Y g(x,y) dy$$ instead of $$\int_X \int_Y f(x) g(x,y) dy dx.$$ If ...
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Hartshorne: Definition of $K^*$ where $K$ a function field of scheme.

Let $X$ be a noetherian integral separated scheme which is regular of codimension one. Let $K$ be the function field of $X$. Now let $f \in K^*$, (I am interpreting $K^*$ to be the set of field ...
$E(X)$ versus $E(X|Y)$
Why is $E(X)$ considered a constant but $E(X|Y)$ considered a random variable? Seems like confusing notation since I'd assume the latter is a fixed constant "the expected value of random variable $X$ ...