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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2answers
47 views

What is the Order (Big O) of this polynomial?

$$\frac{2n^{14} + 7 n^8 - 3}{3n^8 - n^4 + 3}$$ If this division is $p(n)$, I have to write $p(n) = O(n^k)$ I guess the answer is $n^6$, but how can i solve it step by step?
2
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1answer
17 views

Different use of approximate equality symbols

I have been wondering for a long time whether there is a unequivocal way to define and use the symbols commonly adopted for an approximate equality between two quantities. I am a physicist, and I ...
1
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1answer
22 views

What does $L^2((1+|\xi|^2)^sd\xi)$ mean?

In the most elementary contexts of Lebesgue measure, $L^2$ is the space of the lebesgue measurable functions $f$ such that $\int|f(x)|^2dx<\infty$. For a general measure $\mu$, $L^2(\mu)$ is the ...
2
votes
1answer
91 views

What's the real life purpose of Knuth arrows?

I recently read about Knuth's Arrows. Didn't even know those operations existed. My questions is: Do they have real-life applications? Most of the times a mathematical development follows a real-life ...
0
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1answer
13 views

notation for excluding an element from a sequence

I'm working on a question wherein I need to show that $y=Sup\, x_{n}$ but without the element $x_{1}$. Can I just write $y=Sup\, (x_{n}/x_{1})$?
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0answers
15 views

How do I describe the set of all sets that are the result of a given number of changes to a given set?

Let $k$ be the number of elements that are allowed to change in a set with fixed size $n$. How would one formally describe the set of all possible sets that are a result of changing $k$ elements of ...
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0answers
17 views

Is there notation for an open OR closed interval?

Is there a notation for indicating that an interval could be open or closed, (similar to the $\pm$ symbol meaning the operation could be $+$ or $-$)? I am looking for an equivalent, less cumbersome ...
0
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0answers
15 views

In bivariate probability: How do I denote different cases at the same time?

I have two random variables $X$ and $Y$, each of which can take on the values $1$ or $0$. I was browsing other questions for examples of notation, but couldn't find any. In particular I want to know ...
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1answer
35 views

author2vec angle between vectors notation [closed]

Reading the latest "author2vec" paper (Author2vec publication), I stumbled upon equations (1): $h_C^{(x)}=v_u \odot v_p$ and (5): for the sake of this question consider it exactly as (1), where ...
0
votes
1answer
49 views

What's the difference (if any) between writing $(n-1)/2$ and $\frac{n-1}{2}$?

This might be a very basic question, but I've always wondered if there's any difference between these two forms, and under what circumstances may one be preferable to the other?
0
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1answer
27 views

What does the notation $\overline{ \operatorname{span} M}$ represent?

What does the notation $\overline { \operatorname{span} M}$ represent? For example $M$ is total in $X$ if and only if $\overline { \operatorname{span} M}=X$
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1answer
26 views

Is there a shorter way to show the union of many sets?

Let $\space H_n \space$ be a set such that: $$H_{n} = \{ h^2\in \mathbb{N} : n \leq h \leq n^2 \}$$ Where of course $\space n \in \mathbb{N}$. Now if I wanted to specify the union of (for example) ...
1
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1answer
27 views

Difference quotient in little-$o$ notation

I understand that, in the following definition of the derivative, $$f'(x_0)=\frac{f(x_0+\delta x)-f(x_0)}{\delta x}+\frac{o(\delta x)}{\delta x},$$ The term $o(\delta x)$ denotes a remainder. And ...
0
votes
1answer
52 views

What does the overline symbol mean?

So I have got a question in an old exam paper for Fourier Analysis. Let $f:I\to C$ be an integrable function. Prove that$\int_I \overline{f(x)}= \overline{\int_I f(x)}$. The problem is that I ...
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2answers
59 views

What is the meaning of the notation $A :\Leftrightarrow B$?

This is the text from my book: To define a statement $A$ so that it is true whenever the statement $B$ is true, we write $$A :\Leftrightarrow B$$ and say '$A$ is true, by definition, if $B$ is ...
1
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1answer
30 views

What is the definition of a single valued function

this is potentially a dumb question but I am a touch confused about some terminology. I'm reading Ahlfor's complex analysis, and I am in a section on integrals of harmonic functions. I may be being ...
0
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1answer
25 views

What does it mean for a subgroup $H$ of an abelian group $G$ to be less than or equal to $G$?

I am reading through some linear algebra lecture notes and have come across the following notation: $$K \leq G,$$ where $G$ is an abelian group and $K$ is a subgroup of $G$. What does this notation ...
1
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1answer
45 views

Notation and Proof: Sets [closed]

List all eight subsets of the set $$A=\{3,5,7\}$$. Let $$A=\{j,m,h\}$$ Explain why $\{A\}$ is not a subset of $A$. We notice that the given set $A$ is finite. It contains three elements: 3, 5 and 7. ...
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3answers
32 views

Definition of surjective - understanding notation

In Measures, Integrals and Martingales by René L. Schilling surjective (or onto) is defined as: $$f(X) := \{f(x) \in Y\,:\,x\in X\} = Y$$ I think I understand the concept of surjective in a function ...
2
votes
1answer
32 views

Partition $\lambda/\mu$ notation?

When talking about two partitions $\lambda$ and $\mu$, what does the operation $$\lambda/\mu$$ mean? When Macdonald introduces partitions in the first chapter of "Symmetric functions and Hall ...
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0answers
25 views

Are scalar/vector fields basically just “multi-valued” functions?

Not really familiar with terminology in higher Mathematics, so I will try to use python to express my ideas instead. From Wikipedia: a scalar field associates a scalar value to every point in a ...
0
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1answer
16 views

Classes of exponent

I found this terminology in an a paper (link) and did not understand it's meaning. Here is the set of lines that I am talking about: For each prime $p \le g$, we remove all residue classes $\mod p$ ...
2
votes
1answer
57 views

Is there a mathematical symbol for “once”?

I've found a couple symbols that include the concept of once, like "the list of values which appear only once" and stuff like that. Is there a symbol that just means "once" or "one repetition" or ...
2
votes
1answer
30 views

If a word starts with a number, does capitalization apply to the first letter?

If a mathematical word begins with a number and a hyphen, such as "4-dimensional" or $3-manifold," and this word occurs at the beginning of a sentence, should you capitalize the first letter? For ...
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0answers
45 views

How does someone read this notation for a proof?

I've seen this notation in both logic and math and have yet to find a resource that talks about reading it. There's usually a line in between that intersects the two horizontally. Notation: ...
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0answers
22 views

Sum notation $\sum_{\sigma\in\{\pm 1\}^n}$?

I would like to know what the following sum notation means: $$\sum_{\sigma\in\{\pm 1\}^n}\left(\prod_{1\leq i\leq n}F(x_i^{\sigma_i})\right)$$ where $n$ is a positive integer, $x_i$ are some ...
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0answers
19 views

Notation — How do I denote the derivative of a reciprocal evaluated at some value?

Let's say I have a function $f(x)$. To denote the reciprocal, I denote it as $f(x)^{-1}$. If I want to take the derivative of that, I think it's written as $(f(x)^{-1})'$. Then if I want to have that ...
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1answer
106 views

Summation notational convention

Please correct improper notation/terminology $$\sum_{k=0}^{n-1} ar^k$$. $$\sum_{k=1}^{n} ar^{k-1}$$ As far as I can tell these both represent the same thing. It's the partial sum {$S_n$} where the ...
13
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1answer
3k views

What is this type of math notation called? (+ 4 5)

So I've been looking for a general name of this type of mathematics notation (google hasn't been very useful) so that I can learn more about it. Basically, the symbols are in the form of functions and ...
0
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1answer
25 views

Question about $\min(a,b)$ as a notation

What does $\min(a,b)$ mean? Does it mean that it is the minimum of the interval $(a,b)$ or is it the smaller number of the two numbers? Thanks!
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0answers
45 views

Is there a standard notation for coding finite sets of numbers as numbers?

Hajek and Pudlak Metamathematics of First-Order Arithmetic use the Ackermann encoding of hereditarily finite sets, but they use no notation for codes. They let the reader see from context when a ...
0
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1answer
28 views

Notation Inside the Parentheses of a Function

Using the standard notation f(x), if x is strictly 1 or 2, how would this be denoted inside the parentheses? I need to use this notation also for 3,4,5, and 6. Eventually I will need to use it for ...
1
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1answer
27 views

Is anyone familiar with the notation $\sigma|_M$?

I am looking at Ian Stewart's Galois Theory 4th Edition, and unsure about what the notation means. Here's the theorem that the notation is first seen, Suppose $L:K$ is a finite normal extension ...
0
votes
1answer
38 views

Use of quantors/quantifiers and variables in first-order logic.

Let $v_1,v_2,\dots,v_n$ be variables and $\beta$ the variable assignment $\beta(v_n)=2n$ for $n\geq 0$. Of the following, which are true and which false under $\beta$? $\forall v_0 \exists v_1 ...
1
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1answer
21 views

Help with logic notation, what are $S$ and $\underline0$?

This is a more or less literal translation from German, hopefully it's understandable, it's all the information available: Let $L_N=\{\underline0,S,+,\cdot~,<\}$ be the language of the natural ...
0
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0answers
19 views

Correct notation for Cartesian product

I have already seen two notations for the Cartesian product of a family $\{A_{\lambda}\}_{\lambda\in\Lambda}$: ...
0
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1answer
33 views

Decreasing Sigma Notation Sequence

Sorry if this question may seem stupid (I am just fascinated with math), but is there anyway to have a decreasing sequence with sigma notation? Example: 160, 80, 40,...
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0answers
32 views

Understanding multiindex notation and the Sobolev Space $W^{1,p}$.

The notation comes from Evans Partial Differential Equations. From Appendix A, we are given information about multiindex notation. Assume $ u : U \rightarrow R$, $ x \in U$. (a) A vector of the ...
1
vote
3answers
47 views

Math notation question

When I do my homework,I do not understand this notation in below function. The function is Let X be a continuous random variable whose probability density function is: $$f_X(x) = 3x^21_{[0,1]}(x)$$ ...
1
vote
0answers
24 views

Popular symbols for disjointness relation of two sets? [duplicate]

Is there any standard or popular symbol to indicate that two set A and B are disjoint? Of course, it can be described by: But it is still way too long. Is there any popular symbol for the ...
38
votes
5answers
3k views

What does the symbol |_ mean?

For example, (6) The sequence of primes is endless. For, if $p$ is any prime, the number ${\begin{array}{|c}\color{red}p\\\hline\end{array} + 1}$ is greater than $p$ and is not divisible by ...
0
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2answers
71 views

$\log^2n$, $\log n^2$, $\log \log n$, $(\log n)^2$; What are the differences? [closed]

What is the difference between the following: $\log^2n$, $\log n^2$, $\log \log n$, $(\log n)^2$
0
votes
2answers
58 views

How is the Net Change Theorem different from Fundamental Theorem Of Calculus II

1) Fundamental Theorem Of Calculus II $$ \int_{a}^{b}f'(x) = f(b) - f(a)$$ 2) Net Change Theorem $$ \int_{a}^{b}f'(x) = f(b) - f(a)$$ They are the same, why have two?
5
votes
4answers
607 views

Is my current understanding of the fundamental of calculus correct?

My current understanding: part 1) means essentially the integral is the inverse of the derivatve $$\frac {d}{dx} \int f'(x)dx = f'(x)$$ part 2) means essentially we can calculate the integral by ...
0
votes
5answers
67 views

Why do we not include $c$ in the computation of the definite integral?

Why is it when evaluating the definite integral we commonly opt to omit the constant $c$ $$\int_1^2x^2 \, dx= \left.\frac{x^3}{3} \right|_1^2 =\frac{2^3}{3}-\frac{1^3}{3}=\frac{7}{3}$$ But when ...
0
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0answers
27 views

Notation for variables representing complex numbers

Is there a standard way to indicate that a variable represents a complex number? In physics, it is convenient to analyze oscillating systems using complex numbers. The authors of one popular ...
13
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3answers
2k views

What is the difference between the three types of logarithms? [closed]

In complex analysis I came across three types of logarithms namely $\ln$, $\log$ and $\text{Log}$. What is the difference between the three?
1
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1answer
66 views

What is more correct $2^{A}$ or $2^{|A|}$

I saw at mt notebook this: for any set $A$: $$|A|\le |2^{A}|$$ Now I'm wondering, what is the meaning of $2^A$? $A$ is not a number... It doesn't need to be: $$|A|\le |2^{|A|}|$$ or $$|A|\le ...
0
votes
0answers
29 views

How do I write this in sigma notation?

P(x) = 1-x P(x) = 1-(1-x) P(x) = 1-{1-(1-x)} P(x) = 1-[1-{1-(1-x)}] I want to subtract the previous function by 1 each time. How can I write that in sigma notation. The function basically ...
0
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1answer
17 views

Formal notation for $x=^{+}_{-}a+b$

We learned in school that the solution $x$ to the equation $x^2-2x-5=0$ is $x=1\pm\sqrt{6}$. Now if x is being defined as such, the $\pm$ really means the definition isn't expanded fully; to ...