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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3
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2answers
155 views

Textbook determinant convention

My text book is called "Linear Algebra and its applications" by David C. Lay. I am just wondering why the textbook uses the absolute value symbol when it wants us to compute determinants. For ...
1
vote
1answer
722 views

What does the uppercase greek symbol pi mean for sets?

What operation is denoted in e.g.: $\Pi_{i \in I} S_i$ The document in question is: John C. Reynolds - Types, abstraction, and parametric polymorphism Since no index order is specified, the ...
1
vote
1answer
71 views

$\bigcap\limits_{n=1}^\infty A_n$ vs $\bigcap\limits_\infty^{n = 1} A_n$

This is probably a trivial question, but what is the difference between those two? $$\bigcap_{n=1}^\infty = \{x \mid \forall n \in \mathbb N, x \in A_n\}$$ What does the other intersection mean?
1
vote
1answer
168 views

Dual space notation (inner product)

What does the notation $$\langle u, v \rangle_{H^{-1}, H^1}$$ mean? Is it simply $u(v)$ or does it have something to do with inner products on $H^{-1}$ and $H^1$?
0
votes
1answer
76 views

Is there a simpler expression for $f(f(f(…f(x)…)))$ (total n '$f$')? [duplicate]

Is there a simpler expression for $f(f(f(...f(x)...)))$ (total n '$f$') ? Thank you.
9
votes
2answers
199 views

What is the gender of $K(\pi,n)$ in French?

This is a kind of silly question, but I don't know where else to ask. Suppose I wanted to say "Ceci n'est pas une pipe" but with $K(\pi,n)$ substituted for "pipe." Would the article be "un" or "une"? ...
1
vote
3answers
344 views

Modulus of inverse of a number

In the Chinese Remainder Thm., $y_i$ is the modular inverse of $\frac{P}{p_i}$, where $p_i$ is the $i$th modulus in a set of $n$ congruencies and $P$ is $\prod_{i=1}^np_i$ (right?). So if I calculated ...
0
votes
3answers
350 views

Symbol for WLOG

Does anybody know a commonly used symbol for WLOG (without loss of generality)? I'm not comfortable with typing the whole thing every time and the abbreviation is just a compromise. If there is one ...
14
votes
3answers
1k views

Is it possible to write a number in a base of less than 1?

Following on from this question: http://math.stackexchange.com/a/217112/45127 If we take base 10 as an example, the granularity is 1. I.e. we increment the digits in an increment of 1 until we ...
0
votes
2answers
497 views

Is there a symbol for “Time Displacement”

Does the "Time Displacement" property of a wave function have an associated symbol? Amplitude = $\hat U$ Period = $T$ Ordinary frequency = $f$ Angular frequency = $ω$ Phase = ...
0
votes
2answers
49 views

Is this question proper? “Solve $\log_{10}x\in\mathbb{R}$.”

Is this question proper? "Solve $\log_{10}x\in\mathbb{R}$."? I know that $\log_{10}x\in\mathbb{R}$ means $x\in(0,\infty)$, but can we write "Solve $\log_{10}x\in\mathbb{R}$." as a question alone? ...
2
votes
1answer
225 views

Notation: Representer Theorem for Reproducing kernel hilbert spaces

Am studying the basic concepts of RKHS and the representer theorem: In $f(x_i)=<f,k(x_i,\mathbb{.})>$, what does $ f$ on the r.h.s denote? What is its structure-is it a vector? I was thinking ...
3
votes
1answer
256 views

Prove that a formal language is infinite

I'm having trouble with the following exercise: Let $\Sigma = \{a,b,c\}$ and $L$ be a formal language, that consists of all words which contain all three letters at least once. Show that $L$ is ...
1
vote
1answer
290 views

projection operator notation

In my book is stated (in Dutch, but I tried to translate it to English): Let $V$ be a $K$-vectorspace and $q_1, \dots, q_r$ a set of projection-operators on $V : \sum^r_{i=1}{q_i} = 1_V$ and $\forall ...
0
votes
1answer
60 views

Tuple(?) with square brackets

In the context of coding theory, an $[n,k,d]$ linear code is a linear code of length $n$, dimension $k$, and minimum distance $d$. I rarely see it written as "an $(n,k,d)$ linear code". Why? Do the ...
8
votes
5answers
977 views

Why do mathematicians use this symbol $\mathbb R$ to represent the real numbers?

So, I'm wondering why mathematicians use the symbols like $\mathbb R$, $\mathbb Z$, etc... to represent the real and integers number for instance. I thought that's because these sets are a kind of ...
-1
votes
1answer
57 views

If $K$ is a field, what is $K^1$? (notation)

Let $K$ be a field. What does $K^1$ denote? I found this notation in the context of differentials, "Algebraic Curves, Algebraic Manifolds and Schemes" by Shokurov and Danilov, p. 102.
2
votes
0answers
88 views

Where can I find a description of math language symbols?

I am reading math articles. I meet math symbols. For example $\exists$ or $\forall$. For example for "For any a exist e that" can be rewriten as: $\forall a \exists e$ Where can I find full ...
12
votes
2answers
663 views

What do Greek Mathematicians use when they use our equivalent Greek letters in formulas and equations?

Like for example, it's common to use the Greek letter $\theta$ to represent an angle right? So what would a Greek person doing math use to represent an angle? Would they also use $\theta$? Or is there ...
1
vote
2answers
89 views

Prove that $\prod_{i=2}^n (1-1/i^2) = {n+1\over 2n}$

prove the $$\prod_{i=2}^n (1-1/i^2) = {n+1\over 2n}$$ for all n greater or equal to 2. $\pi$ should be a big pi from $i=2$ to $n$ for $(1-1/i^2)$. I'm really confused about the $\prod$ function. ...
5
votes
1answer
2k views

Meaning of mathematical operator that consists of square brackets with a plus sign as a subscript

I was reading a paper on tomographic reconstruction, and I found an operator that is not explained: $[expression]_+$ The operator was used to compute a surrogate for the log-likelihood cost ...
7
votes
1answer
1k views

Why use radical notation instead of rational exponents?

I'm helping my younger sister for her math class. She has recently been taught integer exponents, and has starteed studying radicals (mainly square roots). The next topic will be rational exponents, ...
0
votes
2answers
72 views

Problem with Math Notation

I am getting confused with this notation: $$R =\{x | x=a_i\times b_j;1\leq i\leq m \text{ and } 1\leq j\leq n\}$$ where $a$ and $b$ are vectors of length $m$ and $n$ resp. What does this mean? Does ...
0
votes
2answers
92 views

For any two points, there exist a path of $n$ segments that connects them. Is there a name for this kind of set?

We consider a set $A$. $A$ is called convex if for every $x,y\in A$, we have the line segment $xy$ is also in $A$. I want to generalize this notion, such that instead of one line segment, there can ...
0
votes
2answers
78 views

Exponentation vs Power

What definition of $a^b$ operation is the most popular and standartized: Exponentation or Power? Is any difference between them?
0
votes
1answer
97 views

Why are $321,213,132$ in cyclic order

Could anyone help me understand this concept, if we have $1,2,3$ why are $$123,231,213$$ Considered in cyclic order and $$321,213,132$$ Considered in acyclic order? I am asking this in regards to the ...
1
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1answer
183 views

How can this algorithm be expressed in mathematical terms?

I have found a solution to a basic problem using an algorithm, but I'm having a bit of a hard time expressing this algorithm in terms of discrete math. ...
0
votes
2answers
2k views

Big O Notation and finding witnesses

I am trying to figure out some stuff here with Big O Notation. I mean I understand the concept of it and can generally be able to tell what the efficiency of something is, but I do not really ...
4
votes
5answers
753 views

Does $x/yz$ mean $x/(yz)$ or $(x/y)z$?

When people write $x/yz$, do they usually mean $x/(yz)$ or $(x/y)z$? For example, from Wikipedia If $p\geq 1/2$ , then $$ \Pr\left[ X>mp+x \right] \leq \exp(-x^2/2mp(1-p)) . $$ Thanks!
0
votes
2answers
201 views

Why is Fermat's spiral formula written as $r^2=a^2\theta$ instead of $r=a\sqrt{\theta}$?

I'm reading Clifford A. Pickover's Math Book, in the Fermat's spiral page, it says the Fermat's spiral formula is $r^2=a^2\theta$, why isn't it written as $r=\pm a\sqrt{\theta}$? What's the problem in ...
2
votes
2answers
204 views

When do I write $\sin(x)$ and when $\sin x$?

I sometimes see $\sin x$ and sometimes $\sin(x)$. Are the parenteses needed since the sine is a function or is it more an operator that can be premultiplied to the variable? Or are people just lazy?
1
vote
3answers
161 views

How to denote a function that depends on $a_1, \ldots, a_n$ without the dots?

I know that I can wrote something like $$a_1 + \cdots + a_n$$ without the dots as $$\sum_{i=1}^n a_i$$ which seems clearer to me. As a programmer, I'd rather have a rule set with variables than ...
2
votes
0answers
76 views

What's the equivalent to floor(x) and ceil(x) for real numbers?

Are there equivalents to the notation of $\lfloor x \rfloor$ and $\lceil x \rceil$ that don't round to the next integer, but to a specified digit of a real number? Examples $floorReal(2.3656, 1) = ...
2
votes
1answer
2k views

What is i (mod p)?

Is there a difference between $i$ mod $p$, and $i$ (mod $p$)? To give context, this is the original problem: if $i \geq 0$ what is $i$ (mod $p$)? edit: Forgot to add the parentheses to example
12
votes
4answers
1k views

Why not write $\sqrt{3}2$?

Is it just for aesthetic purposes, or is there a deeper reason why we write $2\sqrt{3}$ and not $\sqrt{3}2$?
0
votes
0answers
780 views

Semi-Factorial Skipping Every $k^\text{th}$ Number

For an integer $n$, the semi-factorial $n!!$ can be defined as $$ n!! = n(n-2)(n-4)\cdots $$ In other words, the semi-factorial of $n$ is the familiar factorial, but with every other term omitted. For ...
5
votes
5answers
261 views

Is there a definition or standard for the symbol $\pm$

In college, I had been taught the famous formula $$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.$$ Here $\pm$ means that I choose either $+$ or $-$. But I have seen sometimes in physics that $\pm$ can mean some ...
0
votes
2answers
108 views

Why is this set of $2 \times 2$ matrices of real numbers a nonabelian group under multiplication?

My book wrote something like this Consider $M_{2}^*(\mathbb{R}) = \left \{ A \in M_{2}(\mathbb{R}) : \det(A) \neq 0\right \}$ $A = \bigl(\begin{smallmatrix} 1 &1 \\ 1 &0 ...
1
vote
1answer
3k views

Notation: Matrix with a prime

I can't find this over the Internet: what does a matrix with a prime mean? A' I found this in an exercise, this is in basic linear algebra.
1
vote
1answer
296 views

little o notation with natural logs

I'm having trouble with little o notation. Help me show that: $2(n^2 + 100n)\log^5n = o(n^2\sqrt{n})$. It is the last hwk on my sheet and I don't understand it, if someone can help me with ...
2
votes
3answers
506 views

big O notation with asymptotically nonnegative increasing functions

Let $f(n)$ and $g(n)$ be asymptotically nonnegative increasing functions. Show: $f(n) · g(n) = O((\max\{f(n), g(n)\})^2)$, using the definition of big-oh. I can't quite figure this out, can ...
1
vote
2answers
69 views

Is there a particular notation for a function confined in a set?

For example $f:\mathbb{R}\to\mathbb{R}$ is a function. How to simply express a correspondent function $g:\mathbb{Q}\to\mathbb{R}$ such that $g(x)=f(x)$, $\forall x\in\mathbb{Q}$?
0
votes
1answer
63 views

infimum - notational problem

I have divided a two-dimensional coordinate system into several regions that form a partition. Now I want to define a line that is formed by the lower bound of some of these regions, and I cannot ...
5
votes
4answers
300 views

What is the correct definition of the absolute value of $x$, $|x|$?

What is the correct definition of the absolute value of $x$, $|x|$? Option A $$ |x|= \begin{cases} -x&\text{if } x < 0\\ 0& \text{if } x=0\\ x&\text{if } x>0 \end{cases} $$ Option ...
3
votes
1answer
222 views

What does $c.c.$ mean in this proof?

This is a proof from Wikipedia of Moore-Penrose inverse being the optimal solution of a least squares problem, in which there is a acronym $c.c.$ occurred in some of the equations. Mind if I ask what ...
0
votes
1answer
82 views

Two $\psi$ functions

This is either a notation/history question or a point of confusion. In (for example) Ramanujan's proof of Bertrand's postulate, he uses the following notation: $\log [x]!$ means $\log ([x]!),$ in ...
1
vote
1answer
459 views

Is there a mathematical symbol for “the value grows”?

Is there a mathematical symbol for "the value grows?" For example: This result will be increasingly difficult as the value of n grows to infinity.
0
votes
1answer
104 views

Is this function valid in the mathematical sense?

I'm trying to find the error in a proof that yields a contradictory result, and I was wondering if the (rather silly and convoluted) function involved in the proof is "valid" in the mathematical ...
2
votes
2answers
197 views

What does $\mathbb R^S$ mean when $S$ is a set? [duplicate]

Possible Duplicate: What's the meaning of a set to the power of another set? What does $\mathbb R^S$ mean when $S$ is a set? I am reading a text and I wonder if it has a special meaning ...
2
votes
3answers
3k views

Symbol for the set of odd naturals?

Obviously the set of naturals is denoted $\mathbb{N}$, but is there a symbol for the set of odd naturals? Would $2\mathbb{N}+1$ (or $2\mathbb{N}-1$) be a standard notation?