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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101 views

Clarification regarding white space in rules of inference

What is the meaning of the white space in the following notation (or what is meant by the rules themselves)? $$\frac{ }{x\ \ \ x}$$ or $$\frac{y\ \ \ t_i}{y\ \ \ ft_1...t_n}$$ Where the white ...
8
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1answer
142 views

Exact sequences with parallel arrows

In Milne's Étale Cohomology (both the book and the online notes), he sometimes says a diagram of the form $$0 \rightarrow A \rightarrow B \rightrightarrows C$$ is an exact sequence if $A \to B$ is ...
0
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1answer
93 views

What does the notation $\mathbb{F}_3[x]$ mean?

What does $\mathbb{F}_3[x]$ mean in terms of polynomials?
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3answers
153 views

Is there a compact notation for indicating the reasons for an implication?

Is there a compact, commonly used notation for indicating the reasons for an implication? For example, suppose I have previously established or been given $P$, and can use it to show that $B$ follows ...
2
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2answers
166 views

Notation for “first $x$ where $f(x)$ greater than $t$”?

What is the preferred notation for expressing the first $x$ where $f(x)$ is greater than a threshold $t$. This is similar to $\arg\max$ notation but instead of max, I want the first $x$ where $f(x)$ ...
3
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1answer
463 views

Centre dot in probability notation?

What does the dot mean in probability notation I sometimes see things like $x \sim P_t(\centerdot \vert x, \theta_{db})$
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4answers
193 views

Understanding the $\equiv$ symbol

I am trying to understand a wierd symbol in a book and I am failing. The symbol is this '$\equiv$'. I understood that if I have $32\equiv 2\bmod15$ means that if I divide $32$ with $15$ I will get ...
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1answer
94 views

meaning of the notations $\mathbb{Z}^{n}$ and $\# (G/2G)$

Does anybody know what the following means? It was never introduced in the lecture... What is the meaning of $\mathbb{Z}^{n}$? And the meaning of $\#(G/2G)$ where $G$ is a additive group? ...
4
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1answer
152 views

Backslash notation: $\Gamma {\setminus} \mathbb{H}^n$

I encountered this notation in a paper by Carron: When X = $\Gamma{\setminus}\mathbb{H}^n$ is a real hyperbolic manifold, ... $\Gamma$ is a discrete torsion free subgroup of SO$(n,1)$. My ...
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2answers
159 views

Regarding a notation related to divisors & elliptic curves

Section 5.8 of the book An Introduction to Mathematical Cryptography defines the divisor of a rational function $f(X,Y)$ defined on an elliptic curve $E: Y^2 = X^3 + AX + B$ as the formal sum: ...
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3answers
362 views

Notation of Dual Pairings and Inner Products

As discussed in this question, any inner product space $(V, \langle \cdot, \cdot \rangle)$ can be considered as self-dual and so a "dual pairing" can be effected via the inner product, e.g., $$ ...
4
votes
2answers
176 views

Trig reciprocal function nomenclature?

The fact that the reciprocal of $\sin\theta$ is $\csc\theta$, and the reciprocal of $\cos\theta$ is $\sec\theta$ messed with my head for the longest time when I was taking trig. Why are the functions ...
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1answer
404 views

Help interpreting a gamma distribution

The following is from an article I'm reading and is the conditional density of a random variable that is distributed according to a gamma distribution, conditional on the value of a parameter $t$. ...
37
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2answers
2k views

What are the rules for equals signs with big-O and little-o?

This question is about asymptotic notation in general. For simplicity I will use examples about big-O notation for function growth as $n\to\infty$ (seen in algorithmic complexity), but the issues that ...
1
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1answer
708 views

Variable naming convention in mathematical modeling

Is there a guide or source of inspiration I can use when picking variable and constant names for a mathematical formula? I'm in the process of converting a poorly written technical document into ...
0
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1answer
69 views

Name of number representation

What do you call a number representation which constists only of integers, arithmetic operators and exponents/roots? I.e. no decimal numbers, trigonometric expressions, etc. EDIT: To clarify, I want ...
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2answers
110 views

Explanation of notation required?

What is the meaning of the notation $sign(k \mod 4)$ where $k$ is a positive integer? The notation can be found, for example in the paper "Minimum triangle-free graphs".
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2answers
134 views

Notation for when x=?, y=?

Is there notation for what is essentially when, for the situation, for example: In the situation when x is 2, y is 21t (edited) Sorry for being brief; if it lacks clarity, please leave a comment and ...
6
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2answers
186 views

Least non-arithmetical ordinal

As I understand, there exists the least ordinal $\alpha$ such that there is no well-ordering of $\mathbb{N}$ which is both order isomorphic to $\alpha$ and is an arithmetical set. Is there a ...
13
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2answers
1k views

Why is “h” used for entropy?

Why is the letter "h" (or "H") used to denote entropy in information theory, ergodic theory, and physics (and possibly other places)? Edit: I'm looking for an explanation of the original use of "H". ...
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2answers
282 views

distributive law in polish notation

On page 18 "Logic as Algebra" Halmos&Givant wrote the distributive law in Polish notation as $$ = \times a + bc + \times ab \times ac $$ I fail to see anything remarkable here, is there a ...
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1answer
158 views

The space $\mathbb{C}[z]$

What does the space $\overline{\mathbb{C}[z]}$ stands for? Does it contain all the analytic functions or there are something else? And what about the closure thing?
5
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3answers
2k views

Is there a shorthand or symbolic notation for “differentiable” or “continuous”?

In basic calculus an analysis we end up writing the words "continuous" and "differentiable" nearly as often as we use the term "function", yet, while there are plenty of convenient (and even fairly ...
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3answers
171 views

What are the additional symbols used in numeral systems with more than 10 base digits?

What would the last digit be in a base 11 system? Base 12? I'm mostly wondering because I was thinking of a base 36 system with digits 0-9 immediately followed by the letters A-Z but I wasn't sure if ...
3
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1answer
746 views

I'm confused: does # mean Q.E.D. or contradiction?

Last week one teacher used the pound sign # for implying that we were done proving something and a different teacher used the same for highlighting a contradiction.
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1answer
60 views

How should I understand $\frac{\partial^2 v_i}{\partial x_j\partial x_j}(x)=\frac{\partial p}{\partial x_i}(x)$?

The formula is from the first paragraph in the paper "Second Kind Integral Equation Formulation of Stokes' Flows Past a Particle of Arbitrary Shape" by Power and Miranda: ... the governing ...
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3answers
1k views

Why does higher level mathematics more often than not use Greek lettering?

In high school, at least from what I've seen, mathematics courses never use Greek lettering in their description of concepts, with the notable exceptions of $\Sigma$ for summations, $\Delta$ for ...
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2answers
467 views

How far do known ordinal notations span?

What is the largest known ordinal number $\alpha$ such that a uniform notation scheme has been developed for all ordinals up to $\alpha$ (there should be no "gaps" in what ordinals are representable), ...
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2answers
297 views

How to write a functional fold in mathematics?

Given is a sequence of natural numbers: $1,2,...,n$. I want to choose two elements $a,b$ of this sequence, calculate $c=ab+a+b$ and write $c$ back to the sequence. After $n-1$ iterations, there is ...
7
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1answer
198 views

Notation for functions vs. numbers

I understand that $f$ represents a function while $f(x)$ represents the value of a function, but while I can easily see how to apply this convention to work with functions instead of numbers in some ...
2
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0answers
106 views

Is there a name for the element-by-element multiplication of two vectors? [duplicate]

Possible Duplicate: Is this Vector operation defined? Does it have a name? I am a software engineer, so bear with me. Suppose I have two vectors of equal length containing numbers. Is ...
2
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4answers
284 views

Union of Uncountably Infinite Sets

How does one notationally describe the set which is the union of uncountably many other sets. For instance, for each x such that a < x < b, where a and b are real numbers, if there is assigned ...
2
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2answers
103 views

Elementary question on Sums notation

I reading on Sums and I am reading about the difference between using a generalized Sigma notation and the delimited form. Ok, I understand that the generalized form is more expressive. But I ...
17
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2answers
21k views

Weird E letter? (sigma) [duplicate]

Possible Duplicate: What does the math notation $\sum$ mean? My school's prescribed book uses the weird letter E character without explaining what it is in the first chapter when it talks ...
1
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1answer
277 views

Simplifying function notation

For example, in the process of proving that $$\left({\frac{f}{g}}\right)'\left({a}\right)= ...
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0answers
133 views

What does 'the subspace W = ( < \{> v_1 \})^o' mean?

Can anyone help me understand the notation used at the end of this sentence? 'Now we proceed to the dual space $V'$, and the subspace W = ( < {> v_1 })^o'
0
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1answer
92 views

How do you format a logarithm's base in Stack Exchange? [closed]

How would you type log [base] (4) in stack exchange?
5
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3answers
403 views

Notation on proving injectivity of a function $f:A^{B\;\cup\; C}\to A^B\times A^C$

I'm trying to prove that for any cardinal numbers $a,b,c$, the following holds: $a ^ {b + c} = a ^ b a ^ c$ i.e. that there exists a bijective function $ f : A ^ {B \:\: \cup \:\: C} \rightarrow A^B ...
1
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1answer
483 views

Index/Einstein notation to derive Gibbs/Tensor relations

In a few continuum classes I have seen indicial notation used to derive relations in Gibbs notation. However, Gibbs notation is valid for all coordinates while indicial notation is valid only for ...
11
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4answers
1k views

What was the notation for functions before Euler?

According to the Wikipedia article, [Euler] introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical ...
7
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2answers
346 views

Why do we treat $\mathrm{d}x$ in the indefinite integral as if $f(x)$ were multiplied by it?

The first explanation I heard for the $\mathrm{d}x$ - it just shows by which variable we are integrating. Which made sense because $(F(x)+C)^\prime=f(x)$, not $f(x)\mathrm{d}x$. Now, some time later, ...
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0answers
243 views

Notation for a sum defined in terms of base 2

First acknowledging the helpful response to the earlier version of this sequence, I have found a complete expression for the sequence in closed form, and would be interested in improvements to the ...
0
votes
1answer
2k views

Definition of a Subspace - Possible to Express with Mathematical Notation?

Theorem: Let V be a vector space over the field K, and let W be a subset of V. Then W is a subspace if and only if it satisfies the following three conditions: The zero vector, 0, is in W. If u and ...
8
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2answers
452 views

Different standards for writing down logical quantifiers in a formal way

What are standard ways to write mathematical expressions involving quantifiers in a (semi)formal way ? In different posts of mine concerning similar question I have encountered for a generic ...
3
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4answers
363 views

What does $\mathbb{Z}_{7429}$ mean?

What exactly does $\mathbb{Z}_{7429}$ mean? Is it the set of all integers up to and including 7429?
1
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1answer
78 views

Closed form for sequence of distributions

This sequence of distributions interests me and I am looking for an expression in closed form. We are looking at populations of size n!. For n=2, we divide the population in half, and assign to each ...
0
votes
1answer
163 views

Where does the % symbol originate from? [duplicate]

Possible Duplicate: What is mathematical basis for the percent symbol (%)? Where does the % symbol originate from?
3
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2answers
91 views

Pronunciation of $M(x)$ and $m(x)$

Suppose I use two functions and I denoted them by lowercase and uppercase letters $m(x)$ and $M(x)$. Of course, I have to distinguish them somehow. How do I read this? Is capital/uppercase $M$ of ...
2
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5answers
250 views

Confused about modular notations

I am little confused about the notations used in two articles at wikipedia. According to the page on Fermat Primality test $ a^{p-1}\equiv 1 \pmod{m}$ means that when $a^{p-1}$ is divided by $m$, ...
10
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3answers
768 views

Who introduced the notation $x^2$?

In the book 'Problem Solving and Number Theory' I read The law of quadratic reciprocity was discovered for the first time, in a complex form, by L. Euler who published it in his paper ...