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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7
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5answers
5k views

Scientific notation and negative numbers

My daughter is learning scientific notation in school, and her textbook says something to the effect of this: Scientific notation is a method of writing numbers as the product of two factors ...
3
votes
2answers
63 views

Notation to use for operation

Lets say I have some numbers: [1, 3, 5, 1, 10, 8] What is the proper mathematical notation for the following operation? $$ (1-3) + (3-5) + (5-1) + (1-10) + (10-8) $$ Here is what I was trying: ...
0
votes
1answer
71 views

Little Notation question

for example I have the equation $2y=4x$ and I want to solve it for $x$, (sure, $x = \frac{1}{2} y$, but how can I just write, that I want to solve it for $x$? Regards
6
votes
1answer
943 views

Subscript in maximum notation

My question is concerning a maximum notation. I have a $3\times 3$ matrix: $$Q=\begin{bmatrix}-3&2&1\\1&-2&1\\0&1&-1\end{bmatrix},$$ where $q_{ii}$ = $-\sum_{i \neq j} ...
1
vote
1answer
55 views

Notation for the sum of the scores of items of an intersection of two sets

I have two sets of items. Every item has a score. I'm finding the sum of the scores of the items of the intersection of both sets. What would the best way to notate this be? An example: ...
1
vote
1answer
68 views

ZFC Union axiom

Maybe I'm just need to buff up on my logic notation, but I don't fully understand the following: $$\exists y\forall z \left(\exists w(z\in w\wedge w\in x)\implies z\in y\right)$$ How should I ...
1
vote
2answers
216 views

Reverse Polish Notation and numbers $>9$

Excuse me for the newbish question in advance but how should I make sure I don't make a mistake converting from RPN to infix notation when I don't know if some of the numbers aren't two-digit ones or ...
1
vote
3answers
104 views

Black Scholes $ ( \;)^+$ Notation Question

Came across an exercise involving the Black Scholes formula which uses: $E[(S_{T}-K)^{+}|F_{t}]$ What is the $\;(\;)^{+}\;$ in the expression? Is this some kind of operator? Thanks.
3
votes
2answers
157 views

Original papers on the subject of group actions

Does anyone if there are any original paper(s) that first introduced the notion of group action or permutation representation, and who the author(s) were? Any references I have found so far on e.g. ...
1
vote
2answers
110 views

Is the index in an nth root allowed to be fractional?

We have nth roots that can be rewritten as fractional powers: $$\sqrt[n] x = x^\frac 1 n$$ I was looking around on Wikipedia and some other online material, but I couldn't find any definitive set of ...
7
votes
2answers
297 views

“Fun” question: anyone know why $e$ (Euler's Number) was chosen for wave functions?

First, let me say that this is merely something I have always wondered about, and can never seem to find a good reference for. I simply want to know... the geek in me. Why was $e$ (Euler's Number) ...
4
votes
3answers
831 views

Where did these symbols come from?

Where did these symbols come from? Like Pi, Fee and this weird E/sideways M and the triangle.
4
votes
3answers
4k views

What does this mathematical notation mean? [duplicate]

Please excuse this simple question, but I cannot seem to find an answer. I'm not very experienced with math, but I keep seeing a notation that I would like explained. The notation I am referring too ...
4
votes
1answer
211 views

Notation: What's $]a,b[$ [duplicate]

Possible Duplicate: Question about set notation Suppose we have that $\ f:]a,b[\rightarrow\mathbb{R}$. What is $]a,b[$? I know what $[a,b]$, $(a,b)$, $[a,b)$ are. I would usually google ...
1
vote
1answer
279 views

Notations in Group theory

I will start by apologizing as many will not like this question. I am reading the paper COHOMOLOGY THEORY OF GROUPS WITH A SINGLE DEFINING RELATION and having focused on typology throughout my ...
0
votes
2answers
50 views

What is $y^{(n)}$, and how do I find it?

The question : Find $y^{(n)}(x)$ if $y(x)=\frac{1}{2-x}$... there is no explanation for $y^{(n)}$ in my textbook...can you explain this to me? First I tried to find the derivative of $\frac{1}{2-x}$ ...
9
votes
4answers
2k views

Meaning of $\geqslant$, $\leqslant$, $\eqslantgtr$, $\eqslantless$

What do slanted inequality signs mean? Specifically, these are $\geqslant$, $\leqslant$, $\eqslantgtr$, $\eqslantless$. Is there any place I can look this up? I've searched Wikipedia and the web and ...
22
votes
7answers
1k views

Notation for repeated application of function

If I have the function $f(x)$ and I want to apply it $n$ times, what is the notation to use? For example, would $f(f(x))$ be $f_2(x)$, $f^2(x)$, or anything less cumbersome than $f(f(x))$? This is ...
1
vote
3answers
1k views

Mathematical notation for length?

I would like to write an equation to sum the values of each number in a vector divided by the length of the vector. What is the proper way to write this formula? As an example, consider vector v: ...
4
votes
2answers
121 views

Relation-preserving maps as morphisms of a category

What is the canonical name for the category whose objects are all pairs $(X, \rho)$, where $X$ is a set and $\rho$ is a binary relation on $X$, and whose objects are relation-preserving maps? That is, ...
0
votes
1answer
63 views

Leaving out the indeterminate in an integral

Let $f,g : \mathbb{R} \to \mathbb{R}$. Is it acceptable to write $\int_a^b fg$ instead of $\int_a^b f(x)g(x)\,dx$ (i.e., would it throw others off while reading it)? The (lack of an) indeterminate is ...
4
votes
2answers
3k views

How to know what the letters mean in math formulas?

For example, see this Wikipedia section on Newton's laws of motion: ...
1
vote
1answer
1k views

Notation for the first element in a set

I'm looking for a widely used notation to describe the first element of a set. E.g.: S = {5, 7,...,123} is the set, and obviously ...
1
vote
2answers
118 views

What does $s^t$ mean in group theory?

For subset $S$ and $T$ of a group, define $ST = \{st|s \in S, t \in T\}$ and $S^T = \{s^t|s \in S, t \in T\}$. What does $s^t$ mean in this context?
1
vote
2answers
224 views

What does means the $\frown$ in sequence notation?

In the theorem 3.6 of Juhász's Cardinal Functions in General Topology appears the following symbol about sequence: $\frown$ The role context of it's appearance is the following: Theorem. Let X be an ...
3
votes
3answers
337 views

Question about set notation

In the following question here the notation $c\in ]a,b[$ is used. What does this mean? I have never seen it before.
0
votes
1answer
27 views

Notation question ($C^r$ curves)

$\mathbf x$ describes a parametrized $C^r$ curve. If $f: \overline{I} \rightarrow I, \overline{t} \mapsto t$ is a valid (I don't know the exact translation, in german it's zulässig) parameter ...
6
votes
0answers
255 views

Notation for n-ary exponentiation

We have $n$-ary sums ($\sum$) and products ($\prod$). Is there an $n$-ary exponentiation operator? $$\underset{i=1}{\overset{n}{\LARGE{\text{E}}}}\, x_i = x_1 \text{^} (x_2 \text{^} (\cdots \text{^} ...
2
votes
2answers
83 views

Simple Question about mathematical convention

For expressions in the form: $$\sum_{i=1}^{k}f(i),$$ does this preclude the possibility that $k$ can be non positive as well as non-integer? Or more explicitly, can I make an induction on $k$? ...
2
votes
1answer
146 views

Limit of an n-ary product

Since a definite integral is defined as $$\lim_{n\to\infty} \sum_{i=0}^n f(x_i^*)\,\Delta x = \int_a^b f(x)\,dx$$ and the integral is much easier to calcluate than a sum, if we change the sum to a ...
0
votes
1answer
68 views

Partial derivative notation: $\left.\frac{\partial \cdot}{\partial\cdot} \right|_{u=T}$

Let $\displaystyle \ \ B(t,T):=\int_t^T f(t,s)ds$, where $f(.,.)$ is a stochastic process whose solution we don't know. My lecture slides make the claim that: $$f(t,T) = \frac{\partial ...
6
votes
2answers
406 views

What does it mean to be a “closed subset of a metric space”?

So I am working my way through the Dover book, Intro to Topology by Bert Mendelson, and in the section on open and closed sets, I'm stuck on the following notation for this problem: Let $(X,d_1)$, ...
4
votes
1answer
165 views

Operators - sums, products, exponents, etc.

$(x + x + \cdots + x)$, where $x$ added $n$ times can be written as $x * n$. $(x * x * \cdots * x)$, where $x$ multiplied $n$ times can be written as $x ^ n$. Is there an operator, such that if ...
2
votes
2answers
117 views

What's the problem with these alphabetic collisions?

I'm reading Halmos' Naive Set Theory. According to the usual and natural convention "for some $y\,(x\, \epsilon \, A)$" just means "$x\, \epsilon \, A"$. It's equally harmless if the letter used ...
0
votes
1answer
240 views

Pullback of a Divisor

Let $f:X \rightarrow Y$ be a finite, separable morphism of curves (curve: integral scheme, of dimension 1, proper over an algebraically closed field with all local rings regular). Let $R$ be the ...
0
votes
1answer
50 views

What are the differences between these two partial derivatives?

given that $z=f(x,y)$ and $x =r\cos(\theta)$ and y = $r\sin(\theta)$ $d^2(z)/d(r)^2$ and $d^2(z)/d(r)$ are both second derivatives of the function $z$? I am getting a little confused with all the ...
11
votes
5answers
552 views

Can anyone explain why $a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}$

I'm so puzzled about this: $$a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}.$$ Why isn't $a^{b^c}$ equal to $a^{(bc)}$? Why is $a^{b^c}$ instead equal to $a^{(b^c)}$? And how is it possible that ...
2
votes
2answers
80 views

Writing functions without 'x' - using only composition and partial-application of other functions?

For example, could the polynomial: $f(x) = x^2 + 3x$ Be written without $x$, using only the exponential, addition and multiplication functions, and high-order functions such as composition and ...
1
vote
1answer
118 views

What does $F^2_n$ mean?

In this Wikipedia entry on Cassini's identity, I saw this equation: $F_{n-1}F_{n+1}-F^2_n=(-1)^n$ $F^2_n$, what does that mean? Is it a summation signs for n to 2? I don't know what it means.
0
votes
2answers
3k views

Notation for “A does not imply B”

I'm looking for a way to express A being true does not imply B. I know that A implied B can be written as $A \rightarrow B$, but what about A does not imply B? $A \not\rightarrow B$?
10
votes
3answers
2k views

Difference between $\implies$ and $\;\therefore\;\;$?

I've seen both symbols used to mean "therefore" or logical implication. It seems like $\therefore$ is more frequently used when reaching the conclusion of an argument, while $\implies$ is for ...
0
votes
1answer
89 views

Equivalence Notation

I am having a difficult time trying to give words to an equivalence, namely, $\preceq$; for instance, how would I word $x \preceq y$? I know it's not that x is less than or equal to y, because ...
0
votes
1answer
200 views

What does RMSD mean?

Normally a rigid superposition which minimizes the RMSD is performed, and this minimum is returned. Given two sets of points and , the RMSD is defined as follows: $$\begin{align*} ...
1
vote
2answers
588 views

mathematical symbol for vector appending

Given a vector $v=<1,2,3>$ I want to have a new vector $v'$, which is the vector $v$, appends with a number $4$. How should I represent $v'$ mathematically? What I wish to have is something ...
0
votes
1answer
112 views

Is there a term for $O( (m+n) \log{mn})$ time algorithms?

Is there a term for $O( (m+n) \log{mn})$? I remember seeing it often in some context but can't remember.
4
votes
1answer
146 views

What is the circumstances of switching to the non-mainstream notation for composition of morphisms?

In mainstream notation for composition, by $g \circ f$ we mean $\operatorname{dom} \left(g \circ f \right) = \operatorname{dom}\left(f\right)$ and $\operatorname{cod} \left(g \circ f \right) = ...
0
votes
1answer
119 views

Don't understand the notation for this group theory question

Could someone explain the notation in this question to me so I can have a go at answering it. Show that $SO_3(\mathbb{F_2}) = \{M \in SL_3(\mathbb{F_2})|M^{-1} = M^t\}$, where $M^t$ is the transpose ...
6
votes
2answers
1k views

How to do \mathbf in handwriting?

I have a bunch of vectors and matrices that are written using \mathbf, eg $\mathbf{w}$ and $\mathbf{W}$. What are standard ways of writing these in hand-writing? I know this is not exactly a maths ...
20
votes
7answers
6k views

How to write \mathcal letters by hand? [closed]

I have a formula in a paper that I want to write out by hand, and it contains two "D"s, a normal D, $D$ in latex, and a 'mathcal', caligraphic D, $\mathcal{D}$ in latex. What are some ...
3
votes
1answer
225 views

What is the difference between these two convergence notations: $f_n \to f$ and $f_n \nearrow f$ or $f_n \searrow f$

I sometimes see this notation for convergence (speaking for functions): $f_n \to f$. And sometimes, I see following: $f_n \nearrow f$ or $f_n \searrow f$. What is the difference between $\to$ and ...