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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Math notation clarification

I'm working on learning more about logistic regression and I came across an equation with some confusing notation that I've never seen before: $$ \frac{\delta}{\delta \theta_{y'}^{(j)}} l(\theta) = ...
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0answers
10 views

Alternative single-letter notations in statistics

I'm learning about statistics, and a thing that is difficult for me is the common use of multi-lettered variables and functions. For instance Standard Error of $\beta$ is written $SE(\beta)$ and the ...
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7answers
987 views

Is an empty parenthesis a valid mathematical expression? [on hold]

Is using an empty parenthesis valid? For example, $15+()=15$. What is the meaning if it is valid? I need an academic reference to validate this.
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1answer
23 views

Vector notation for shifting the elements of a vector

I'm looking for a suitable notation to express a "shift operator" which shifts all elements of a vector forward and sets the first element to zero, e.g., $$\begin{eqnarray*} (1,1,0,1) & ...
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2answers
47 views

Use of brackets around the integrand

Quick notation question: When using brackets after an integral sign, should the brackets enclose just the integrand or everything - the integrand and the differential, i.e. is it: $$\int ...
3
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3answers
66 views

Is there a symbol for “given” in mathematics?

Is there a symbol for "given" in mathematics? For example, for the statement: Each member, $x$, of the integer sequence $f(n)$ equals the sum of the two previous members, $f(n-1)$ and $f(n-2)$, ...
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0answers
12 views

Questions regarding notation (multiple variables, rounding)

I am calculating the coordinates of the Center of Gravity for a 3D volume using the following pseudocode (where A denotes the dimension length and cogA denotes the COG for that dimension) ...
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0answers
16 views

Complex exponential argument to a function

In many texts on signal processing, the following notation is used to describe the Fourier transform of a discrete time signal $x$: $$ \hat{X}\left(e^{j\omega}\right) = ...
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4answers
63 views

What does $T:V\to W$ mean in vector spaces?

What does the sign $\to $ mean in contexts like: "show $T:V\to W$ is an isomorphism" or "if $T:V\to W$ is a linear transformation"...
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2answers
42 views

Sigma Notation multiple sigma

I'm an engineer students, I want to now the runtime of loop inside loop, I get the calculation in sigma notation like the picture above. Can somebody explain to me how sigma inside sigma can be like ...
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1answer
18 views

How to denote a function of all but one parameter (notation question)

Say I have $n$ variables, $x_1,\dots,x_n$ and $n$ functions $f_i$ such that $f_i$ is a function of $x_1,\dots,x_{i-1},x_{i+1},\dots,x_n$, but not $x_i$. Is there a more compact way of denoting this ...
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2answers
19 views

notation for Sumation of Sumation for only for odd iterations

I need to write a summation in summation whether the inner summation should iterate from one through all odd numbers to the teration of the outer summation which goes from 1 to $\infty$... Something ...
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0answers
29 views

What does R[-a,a] represent?

More precisely: $f \in R[-a,a]$. All I could find was related to the symbol $\mathbb R$, but I have never seen it in this particular constellation, and even if it stood for "$\mathbb R$", I wouldn't ...
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1answer
32 views

How to notate the final element in a sequence?

I'm having troubles putting this in to words here, but here it goes: If I have a sequence of numbers, called $A$ where $A$ is a sequence of numbers that don't seem to have a pattern, how can I notate ...
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1answer
35 views

It is okay to have a conditions in a summation limit that depend on the current value of another summation

this is one of those things that I know how to do in a programming environment but not sure how it translates into mathematics. I'm trying to express a sum so that it is easily visible that certain ...
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0answers
26 views

Seeking after notation for two objects equal up to a constant

Sometimes we want to express that two objects are equal up to a constant but there is no need to keep writing out the constant or constants. For example, often times the constant or constants involved ...
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2answers
31 views

$\wedge$ in set builder notation

Wikipedia says to use $\wedge$ in set-builder notation like $\{x \,:\, x > 3 \wedge x \neq 10\}$. However, I prefer to merely seperate predicates by a comma. Which notation is more common?
2
votes
3answers
90 views

What set does $\mathbb W$ denote?

What set does $\mathbb W$ denote? I know this may horribly lack context, but I've seen multiple times on M.SE $\mathbb W$ used in some fairly elementary context I think.
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0answers
52 views

What's the difference between $Df$ and $Tf$?

I'm reading Michael Shub's Global Stability of Dynamical Systems. In chapter 4, he defined hyperbolic set and said the splitting $E^s$ and $E^u$ are $Tf$ invariant. So I assume this $Tf$ is the ...
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3answers
45 views

Help With Notation In Fermat's Last Theorem

The following is the notation for Fermat's Last Theorem $\neg\exists_{\{a,b,c,n\},(a,b,c,n)\in(\mathbb{Z}^+)\color{blue}{^4}\land n>2\land abc\neq 0}a^n+b^n=c^n$ I understand everything in ...
2
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0answers
29 views

Where can I learn more about the “else” operation / “else monoid”?

(The set of natural numbers $\mathbb{N}$ starts at $0$ for me.) Let $X$ denote a set, and define $X_\bot = X \uplus \{\bot\}.$ Let $\mathbf{else}$ denote the binary operation on $X_\bot$ defined as ...
4
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1answer
64 views

Need Help Understanding Notation With Functions

Original picture: LaTeX approximation: $$f\color{blue}{\substack{(x)\\x\to\infty}}=\pm\sqrt{\frac{(x^2+x)^3}{\pi}}.$$ What does the notation highlighted in blue mean? I understand that ...
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1answer
22 views

Representing Several IF statements inside a FOR loop in Math Notation

I wish to correctly represent several IF statements within a for loop in math notation. The FOR loop can be represented as: ...
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0answers
51 views

How to write the family of sets whose elements are the sets in a sequence of sets

I am wondering, given a sequence of sets $( X_n )$, how do we write the corresponding family of sets whose elements are the sets in the sequence? Of course, the same question applies to nets as well. ...
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0answers
20 views

Notation for the set of all integer partitions

I'm working on a project that involves that set $P = \{\{n_1, \ldots, n_k\} \mid k \in \mathbb{N}, n_i \in \mathbb{N} \text{ and } n_1 + \cdots +n_k = n\}$ of all integer partitions of a number $n$. ...
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1answer
34 views

Meaning of $t \mapsto \phi_t(x)$

The context may well be of assistance: Consider a differential equation $x'=f(x)$. Assume that $f:\mathbb R^n\to\mathbb R^n$ is continuously differentiable. Denote by ...
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1answer
27 views

How's this inertia called?

Let $E/F$ be an algebraic extension. Let $L_1,L_2$ be algebraically closed fields and $\sigma_1:F\rightarrow L_1,\sigma_2:F\rightarrow L_2$ be field monomorphisms. Define ...
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2answers
74 views

What does ''$\le$'' mean here?

What does ''$\le$'' mean here? Do you know the meaning of $\le$ in the second last line in the text below? The sequence $0\to N \to M \to M/N \to 0$ is exact, so by Problem 5, the sequence $0 ...
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0answers
34 views

The notation of mathematics stands to mathematical meaning as $x$ stands to $y$. What would you fill for $x$ and $y$? [closed]

What is the relation of the notation of mathematics to the meaning behind it? So for example how would you put it? The notation of mathematics stands to mathematical meaning as $x$ stands to $y$. What ...
0
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1answer
16 views

Conway polyhedra notation calculator?

I recently read about Conway polyhedra notation, and I want to experiment with it. Are there any programs that take the notation, and output a representation of the shape?
0
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2answers
27 views

Symbol to denote the angle between two points

Let $p = (0,0)$ and $q = (1,1)$ be two points. I would like to denote the angle between these two points ($45^\circ)$. I took a look at the lists of symbols and the symbols $\angle$ and ...
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1answer
69 views

Which one of the following logical propositions is to be preferred?

I'm trying to update the symbolism of Giuseppe Peano's "Arithmetices Principia", to make the translation freely available. Might I ask you, which of the following might be a correct mathematical ...
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1answer
41 views

In Ring Theory, does a 'power' of a morphism represent composition?

Say there is a ring homomorphism, denoted by $\theta$. If the notes use the expression $\theta^2$, then are they referring to the composition of the $\theta$ homomorphism with itself?
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0answers
19 views

Is there a standard notation for $(p_i-k)(p_{i-1}-k)(p_{i-2}-k)\cdots$ where $k$ is a small positive integer

For $k=0$, there is: $p_i\# = (p_i)(p_{i-1})(p_{i-2})\cdots(5)(3)(2)$ For $k=1$, there is: $\varphi(p_i\#) = (p_i-1)(p_{i-1}-1)(p_{i-2}-1)\cdots(5-1)(3-1)(2-1)$ Is there any other notation that ...
2
votes
1answer
42 views

The mysterious $\dot{H}^{-1}$ notation.

I have encountered the $\dot{H}^{-1}$ notation in one of the SIAM Journal on Mathematical Analysis articles. It appears to be standard (or at least not uncommon) to use this one in the field, since ...
3
votes
1answer
71 views

What does the notation $\mathbf{R}^\mathbf{R}$ mean?

I was reading the Princeton Review of GRE math subject test (4th edition), and one question was (page. 251) Example 6.24 Is the ring $\mathbf{R}^\mathbf{R}$ an integral domain? ...
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2answers
53 views

Notation issue - Asymptotic behaviour: is $\sim$ too restrictive?

As a student I am completely unable to understand unambiguously what is meant by a notation such as $$f \sim g $$ when in Physics the behaviour of two functions at infinity is evaluated. I found a ...
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2answers
71 views

Differential $dx$

I have some trouble understanding a thing. I will reproduce two texts from two different books. In the first, the author defines the function $T:\mathbb{R}\longrightarrow \mathbb{R}$, ...
0
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1answer
39 views

Equation that defines multi-dimensional polynomial

In two-dimensions a complete n-th degree polynomial is given by $P_n(x,y) = \sum_{k=0}^{n}\alpha_kx^iy^j \qquad i+j \leq k \qquad (1)$ . However, now I am dealing with the following two-dimensional ...
5
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1answer
83 views

What does a single-line superscript left arrow mean?

I'm pretty sure it's a limit but I haven't been able to find any page explaining this notation (see below). It's from a paper on block maxima. 3 out of 5 occurences: $V=(-1/logF)^\leftarrow$ (p.4) ...
3
votes
2answers
27 views

Set Notation help?

If $A=\{a_1,a_2,\dots,a_7\}$ and we want to know how many $3$ element subsets exist in $A$, would we simply use ${7\choose3}=35$ on a calculator, or does this notation not account for the empty set, ...
2
votes
2answers
56 views

I've been told that writing $x\equiv a,b,c \pmod d$ is abuse of notation, is it really?

I've been told that writing $x\equiv a,b,c \pmod d$ is abuse of notation, and that I should always write: $$ x\equiv a\pmod {d}\text{ or }x\equiv b\pmod {d}\text{ or }x\equiv c\pmod {d} $$ How true ...
0
votes
1answer
14 views

Argmax as the parameter of a function?

Let $P = \{p_1,\dots,p_n\}$ and $Q = \{q_1,\dots,q_n\}$ be two sets of points and $d(p,q)$ a distance function between points. Given an element $p_k$ I would like to know which is the maximum distance ...
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1answer
27 views

Notation for a statistic, or function of a random variable

A statistic is a function of random variables, so it is also a random variable. Suppose we have a collection $X = (X_1, X_2, \dots, X_n)$, where $X:\Omega \to \mathcal{X}^n$. There are two common ...
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3answers
36 views

Strict ceiling and floor notation

The normal ceiling and floor functions, denoted $\lceil x \rceil$ and $\lfloor x \rfloor$ respectively, refer to the smallest integer greater than or equal to $x$, and similar for the floor function. ...
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1answer
43 views

Why using $v^T \cdot u\text{ instead of simply } v \cdot u$?

I know they are equivalent, but why and when should we prefer using $v^T \cdot u$ instead of simply $v \cdot u$, when $v$ and $u$ are vectors of $\mathbb{R}^m$, for example?
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2answers
64 views

Why do they use absolute value symbols for $|z|=r$ considering any number squared is positive?

Am I right in saying that the absolute value symbols act like a function such that if $x$, for example, is $x<0$ then $x=-x$ In other words $x$ will be positive regardless of what value you give ...
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2answers
37 views

How should trigonometric expressions be simplified?

I have been learning trigonometric identities and I am having trouble understanding how they should be applied to simplify expressions. For example, the expression $2\sin{x} \cos{x}$ is equal to ...
0
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2answers
53 views

How should this equation be read, $|z+1+3i|=|z-5-7i|$

$$|z+1+3i|=|z-5-7i|$$ $z$ represents a complex number right? Then if $$|z+1+3i|=0$$ $${\implies}|z|=|-1-3i|$$ In which sense does this $$|z+1+3i|=|z-5-7i|$$ imply, $$\implies|-4-4i|$$ But $z$ has ...
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3answers
49 views

What's the difference between $\sum_{r=1}^n(ar+b)$ and $\sum_{r=1}^nar+b$

Does $$\sum_{r=1}^n(ar+b)=\sum_{r=1}^nar+b$$ or does $$\sum_{r=1}^n(ar+b)=\sum_{r=1}^nar+\sum_{r=1}^nb$$ If I'm given $u_r=ar+b$ how would I substitute that into $$\sum_{r=1}^nu_r$$ Does that mean ...