# Tagged Questions

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### What is the difference between a sequence of functions $(f_n)$ and a sequence of functions $f_n(x)$?

What is the difference between a sequence of functions $(f_n)$ and a sequence of functions $f_n(x)$? I am reading my textbook on analysis, and it seems to use 'sequence of functions' to describe both ...
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### What does this $\asymp$ symbol mean? (subject: analytic number theory)

I'm reading a survey article by Andrew Granville on analytic number theory. On page 22 of the paper, there appears a strange looking symbol, undefined. I've circled it in red in the screenshot ...
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### Notation for near optimal solution

Usually, $x^*$ is used to denote the optimal solution to a maximization problem. I need a notation to describe a solution that is not optimal but "good enough." In my case this solution is the first ...
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### Notation Question (Meaning of double inclusion symbols)

What does the notation $\subset \subset$ mean? In my class notes, our prof writes $\Omega \subset \subset \mathbb{R}^{n}$ to mean that "$\Omega$ is a convex subset of $\mathbb{R}^{n}$". Is that all ...
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### Sequence Notation in Analysis

If real sequence is a function from the set $\mathbb N$ to the set $\mathbb R$ and function is represented by $(a,b)$, where $a$ is domain and $b$ is range, then why do we represent sequence only by ...
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### Question about notation in differential equations.

In general, an ordinary differential equation is in the form $$\begin{cases} x'(t) = f(t, x(t)) \\ x(t_0) = x_0 \end{cases}.$$ When proving the existence and uniqueness theorems, an operator $T$ was ...
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### Small symbols behind parantheses

I am currently reading the following paper where the author uses constantly small symbols after parantheses, but I do not know what this means. I am particularly interested in equation (23), so you ...
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### Notation Clarification of Koch Curve

I am having trouble making sense of the notation used to describe the Koch Curve in the book Getting Aquanted with Fractals. The link will take you to a preview of the book which describes the ...
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### What does $C^{\text{1,stw}}(0,b)$ mean

I know that this C with the one means continoulsy differentiable functions but what does this stw stand for? Does anyone know this?
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### Product rule smart notation

Imagine we have a product of functions $f_1\cdots f_m$. We know a rule to compute the derivative. On the other hand, we also have a rule or formula to compute the $n$-th derivative of $fg$ but my ...
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### What does $C[0,1]$ mean?

In the context of real analysis, I have found this question: For each $$f \in C[0,1]$$ there is a series of even polynomials , which converge uniformly on $[0,1]$ to f. What is $C[0,1]$ ? Is it ...
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### Given a function space with a norm , what is the meaning of writing $||.||$ when the used norm is $||.||_\infty$

Example 1 Given $$C_{0}(\mathbb{R}^{n})=\{f\in C(\mathbb{R^n} \ | \ \ \exists R \ge 0 \ \text{such that } f(x)=0 \ \text{for} \ ||x||\ge R \}$$ and $$||f(x)||_{\infty} = \max_{x\in R^n}|f(x)|$$ ...
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### Understanding Set Notation

I'm having some trouble understanding a definition and explanation in my textbook Introduction to Analysis by Edward Gaughan 5th edition. The book begins with some preliminary information about sets ...
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### Nowhere dense notation confusion

The text Foundations of Mathematical Analysis by Johnsonbaugh and Pfaffenberger defines nowhere dense as $X$ is nowhere dense in $M$ if $X^{-,-} = M$. What does this mean?
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### How do I read this?

I received the following equation. It is supposed to contain clues to something I have to solve. I am not familiar with the math symbols used here. How do I read the following: ...
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### Weighted average vs. weighted mean

Is there a formal difference between weighted average and weighted mean? I get corrected to the latter if I type in the former in wikipedia, and then there is a lot of stuff about the name "average" ...
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### Notation question (shorthand for dot products?)

I am reading a paper and trying to understand a calculation and all of a sudden I bump into the following term: $D^2_y p(t,y(t,x))(\partial_t y(t,x),y^\epsilon(t,x))$ where $p$ is a scalar field ...
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### indicator function?

Does anyone know what $1_\omega v$ means where $v \in L^2((0,T) \times \Omega )$ and $\omega \subset \subset \Omega$? It should be an indicator function of $(t,x)$, but not sure how to interpret ...
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### Meaning of $C(I,\mathbb{R})$ and $C^{\infty}(I, \mathbb{R})$ related to continuous functions
What does this mean: ($f$ a function, $I$ an interval and $R$ the real numbers) $f \in C(I,R)$ Does it mean $f$ is an element of the collection of continuous functions with domain $I$ and range $R$ ...
This is a newbie question, but I would be grateful for any reference that you could give. let $f(x) \in \mathbb{A}$, where $x \in \mathbb{A}$ Is there a symbol to indicate the repeated application ...