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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24
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7answers
5k views

Is $\exp(x)$ the same as $e^x$?

For homework I have to find the derivative of $\text {exp}(6x^5+4x^3)$ but I am not sure if this is equivalent to $e^{6x^5+4x^3}$ If there is a difference, what do I do to calculate the derivative of ...
0
votes
1answer
19 views

Terminology for when a variable is implicitly a member of some set?

I have sets $N = \{1, \ldots, n\}$ and $M = \{1, \ldots, m\}$. When referring to a generic element of these sets, I typically use variables $i \in N$ and $j \in M$. Is there any standard ...
1
vote
0answers
19 views

How to create a set with the results of a function?

Let $A$ and $B$ be sets of elements and $f()$ be a function that according to a condition return one or more associations $(a_k,b_k)$ that comply that condition otherwise if there is not any ...
1
vote
1answer
52 views

Mixing definite and indefinite integrals

If I have the differential equation $\frac{d^2 y}{dx^2} = f(x)$ and integrate once using indefinite integrals $\frac{d y}{dx} = c_1 + \int f(x) dx $ then apply the boundary condition $\frac{d ...
1
vote
1answer
45 views

Notation help abstract algebra

If $R$ is a ring and $x$ is an indeterminate, what does the notation $R(x)$ mean? I've seen $R[x]$ but not $R(x)$.
0
votes
0answers
35 views

What is the meaning of Lagrange Multiplier in this formula?

Consider $$F = L'VL + (L' X − K' )\Phi$$ $L$, $V$ and $K$ are matrices. $F$: function notation $\Phi$: Lagrange Multiplier, imposes the restriction $L' X = K'$ What does Lagrange Multiplier mean in ...
1
vote
0answers
62 views

Question on notation (topology & fiber bundles)

This is a very elementary question but I can't quite seem to track down a worthwhile source, so I was hoping someone more knowledgeable than I could lend their superiority. In Moore & Schochet's ...
0
votes
2answers
467 views

Scalar notation to vector notation for a system of equations

I have a ($1 \times n$) row vector $\boldsymbol{x}$, an ($n \times n$) matrix $\mathbf{F}$, and an ($n \times n \times n$) tensor $\mathbf{Q}$. I also have a system of equations that reads ...
0
votes
0answers
32 views

Equality notation query

I want to say that $a=b$ and $c=d$ but $a\ne c$. Is this a valid expression: $a=b\ne c=d$?
2
votes
3answers
125 views

What does this notation mean? $x \mapsto f(x)$

What does this notation mean? $x \mapsto f(x)$ I've seen it at the beginning of functions but don't know what it is.
0
votes
1answer
37 views

Set notation - products of subsets

In terms of conventional set notation, a set and it's corresponding power set of cardinality $2$ can be defined: \begin{align} &A&=\quad&\{a,b,c,d\}&\\ ...
2
votes
2answers
128 views

Which rule is applied to define the operator precedence for factorial

Please apologize the question, I struggled with finding a good formulation in the first place: Looking at $\binom{2n}{k}$ it is very clear that for n,k integer and n>k we can solve it by calculating: ...
0
votes
1answer
53 views

Exponentiation for hash function & associativity

Some cryptographic papers use $H^n(x)$ to mean $H(H^{n-1}(x))$ where $H^0(x) = x$ and $H$ is a cryptographic hash. So $H^3(x)$ would be $H(H(H(x)))$. Is this definition formally correct? It seems to ...
0
votes
1answer
77 views

How to denote the minimal bounding curve of two intersecting function curves?

If there are two functions $y=f(x)$ and $y=g(x)$, $x,y\in\mathbb{R}$, how could I denote the minimal bounding curve of these functions? (See the green dotted line on the figure.) I'm looking for an ...
0
votes
1answer
55 views

Notation for a derivative

I am interested if there is notation for a derivative that is in between a total derivative and partial derivative. The total derivative of $f(t,x,y)$ with respect to $t$ is $$ ...
0
votes
0answers
75 views

'Is true' in maths notation?

I want to write the following statement in only maths notation without any words: $$\sum^n_{r=1}r=0.5n(n+1)$$ is true for all positive integers n. This is what I have got so far. ...
1
vote
0answers
43 views

Product over real interval? Is there a better way of putting this?

In my amateur interest, I have arrived at this (nothing rigorous here at all):$$\prod_{a\in [1,2]} \prod_{b=0}^\infty f(a,b) \neq 0$$ For starters, there might be a more intuitive way about doing ...
1
vote
1answer
138 views

Is there a notation for “open subset”

I very often have to write something like: $\exists U,V\subseteq M$ where $U,V$ are open, but there's no short hand for it. On my written notes, I do tend to write something like: $\exists ...
2
votes
3answers
39 views

If $f$ is a uniformly continuous function show that $g = f(x) - f(y)$ is uniformly continuous on all of $\mathbb{R}^2$

Problem statement: Let $f: \mathbb{R} \to \mathbb{R}$ be a uniformly continuous function on $\mathbb{R}$ and let $g: \mathbb{R}^2 \to \mathbb{R}$ be defined by $f(x) - f(y)$. Then $g$ is uniformly ...
0
votes
4answers
142 views

Which is more preferable to write $\log(x)$ or $\ln(x)$ [duplicate]

Which one is more preferable to write when you are writing an exam. Is it $\log(x)$ which denotes the natural logarithm or is it $\ln(x).$
2
votes
1answer
98 views

What does the sign “$=$” exact meanings?

How can I understand the sign "$=$" from the following expression: $$\mathcal{o}f((x))=\mathcal{o}f((x))+\mathcal{o}f((x));$$ $$\mathcal{o}(kf((x)))=\mathcal{o}(f(x));$$ ...
0
votes
0answers
56 views

Is there a notation for a set of angles?

Suppose that $f:[0,180]\to[-1,1]$ given by $\theta\mapsto\cos\theta$ I wondered whether there was a notation for this domain, the principle values of a trig function? For example we would use ...
4
votes
3answers
181 views

Integration by substitution notation question

Often with integration by substitution I see (and use) the notation $ x \to \frac{\pi}{2} - x $, for the simple reason that I don't have to rename the variable that I am integrating with respect to, ...
1
vote
1answer
51 views

What does the notation $\frac{\partial(x,y)}{\partial(u,v)}$ mean?

Suppose G$(u,v) = (x, y, z)$ In terms of derivatives, what does $\frac{\partial(x,y)}{\partial(u,v)}$ mean?
3
votes
5answers
206 views

What is the difference between the relations $\in$ and $\subseteq$?

What is the difference between the relations "$\in$" and "$\subseteq$" ? Don't they both mean that something is an element of a set? Are they interchangeable in some or all situations? Like: $x \in ...
3
votes
2answers
80 views

Why is there no symbol for rounding to different precisions?

I was taught in a school that one uses rounding for different precision with just the symbol $\approx$, like $13.46\approx 13.5$ or $13.46\approx 13$ depending on the situation. Why are there no ...
1
vote
3answers
672 views

How to show range in equation for multiple variables?

I'd like to show in the below equation that variables $i$ and $j$ need to be chosen from the range $1$ to $n$, but I am not sure how to properly show this. Can somebody please show me the proper ...
0
votes
0answers
34 views

Big $O$ notation and computations

Here all the functions of natural numbers are positive.$p$ is a prime number. Let $A(n)+B(n)=C(n)+D(n)$ where $B(n)=O(p^{5n})$. $ A(n)$ is always less that or equal to $C(n)$.$D(n)$ is known to be of ...
1
vote
1answer
246 views

Which way is best to solve: $T(n)=5T(n/5) + n\;?$

I'm not sure which way is best to solve $$T(n)=5T(n/5) + n$$ (recursion tree/master method/recurrence?) I would like some assistance, which way is easier and how can I be sure I got the right answer ...
0
votes
0answers
74 views

What's the meaning of the $\Sigma^{-1}\;?$

What's the meaning of the $\Sigma^{-1}\;?$ I studied years ago that means (calculates) something special, so I wrote it down. But I can't find its meaning What's the meaning of it in matrix ...
2
votes
1answer
148 views

Is a list and an ordered set (or multiset) the same thing in mathematics?

I've wondered whether a list is the same as an ordered set (or multiset) in mathematics ? Since a list can contain the same element more than once, the above can only be true for an ordered multiset ...
1
vote
0answers
82 views

Notation to represent the columns of a matrix

I have a matrix $\mathbf{Q}$ and would like to represent the $j^{th}$ column-vector of this matrix. Is there a standard mathematical-notation to do that? I have seen things like $Q_{*j}$, but I am not ...
1
vote
0answers
57 views

Best books about notation

I am reading A History of Mathematical Notations and I would love to read further about the trends and advantages of different notations in mathematics, pure or applied. Is there any good book or ...
0
votes
0answers
42 views

Derivative Notation as a factor

In the figure below, the author uses the notation D to replace the Leibniz's notation d/dt, and after that he rewrites the equation, disconnecting the symbol of the derivative, D, of its function, ...
1
vote
1answer
27 views

What is the notation (if any) for series probability inclusion?

In statistics, what is the notation to use for an event $A$ in $B$ in $C$ in $D$, etc., where the series may continue for a large number of events? The following works for a few events: $$A\cap B\cap ...
3
votes
0answers
135 views

Funny translations of mathematical words [closed]

As already noticed in this question there are some mathematical words that literally translated from a language to english (or from english to this language) means something totally different. A few ...
0
votes
1answer
125 views

How to translate math technical terms?

What is a good way to translate mathematical technical terms? This can sometimes be hard because some words have different meanings in some language. For example: "eigenwert" (= "eigenvalue" ...
1
vote
1answer
46 views

Conditional Probability Notation

I am writing a piece of work and have a situation where I have a 'double' conditional. e.g. The event of Y = y conditional on X = x; the event X = x is also conditional on parameter z. What's the ...
0
votes
1answer
68 views

Question about necessary and sufficient conditions?

I am working on a question which begins with The number $\alpha$ is a common root of the equations $x^2+ax+b=0$ and $x^2+cx+d=0$. Given that $a\neq c$, show that $$\alpha=-\frac{b-d}{a-c}$$ ...
1
vote
0answers
18 views

Flow Notation over Interval

Given a section of the flow $\Phi^t(x_0)$ (for finite $t$), I'd like to denote a subsection of this flow from times $\tau^{i-1}$ to time $\tau^{i}$ using similar notation. I was considering using ...
0
votes
1answer
32 views

Specific order sequence as subset of other sequence

I have a certain fitness function that evaluates a sequence. An example of such a sequence is: $h = [2\ 3\ 7\ 5\ 4\ 6]$. The fitness function is defined to be $0$ if the route $h$ does not include the ...
0
votes
2answers
26 views

Describing Notation of a set with an odd gradient

Hello how can you describe such a set: M = { 1 2 5 10 ...} The gradient is always odd in steps of 2 Gradient 1 + 3 + 5 + 7 + ... How can you describe such a set? I need somehow 2 variables to ...
-1
votes
2answers
70 views

Is there a proper term for these?

The 'square root' sign is formally the 'radical symbol'. 'Brackets' are formally 'parentheses' Is there a formal term for the 'fraction sign' or say the 'absolute value bars'? EDIT: I can see some ...
2
votes
0answers
31 views

Can I denote $f'(g(x))=\frac{\text{d}}{\text{d}(g(x))} f(g(x))$?

Can I denote $f'(g(x))=\frac{\text{d}}{\text{d}(g(x))} f(g(x))$? Wikipedia avoids this by letting $y=f(u), u=g(x)$ and then denoting $f'(g(x))=\frac{\text{d}y}{\text{d}u}$.
3
votes
4answers
169 views

What does P in blackboard bold type of letter stand for? ℙ?

In the first post of the thread "Cardinal number subtraction", Cardinal number subtraction there is a symbol for some kind of set which looks like this: ℙ I am familiar with symbols for natural ...
1
vote
0answers
64 views

Notations for interior product

There are two symbols in the Unicode "Supplementary Mathematical Operators" range whose names intrigue me 2A3C: INTERIOR PRODUCT: ⨼ (like $\lnot$ upside down) 2A3D: RIGHTHAND INTERIOR PRODUCT: ⨽ ...
2
votes
0answers
178 views

About the differential notation in measure theory

Is there any good reason for which integrating according to a measure includes a $\mathrm d$ as in $\int f\mathrm d\mu$ ? Or is it just a manner to keep formal consistency with the traditional ...
2
votes
1answer
50 views

In notation for argmin

I saw this notation for $\in$ -- I'm assuming this means "defines", right? $$\hat{\theta} \in \underset{\theta}{\operatorname{argmin}} \dfrac{1}{2} \sum_{j=1}^n (\theta^T x^j - y^j)^2$$ Does anyone ...
2
votes
2answers
29 views

general sum notation considering also not incremental indexing

I need to write a formula with summation in a general case allowing also the case with not incremental indexing. Example: $ \sum_{i=\underline{i}}^\bar{i}$ where can be ...
1
vote
1answer
69 views

Is $\frac{1}{ \frac{1}{x-1}}$ equivalent to $x-1$ when $x=1$?

Is $\frac{1}{ \frac{1}{x-1}}$ equivalent to $x-1$ even when $x=1$?