8
votes
Accepted
What does $\cos \operatorname{am} $ mean?
It's the Jacobi amplitude. See https://en.wikipedia.org/wiki/Jacobi_elliptic_functions#Definition_in_terms_of_inverses_of_elliptic_integrals
4
votes
Accepted
What does $\mathbb{N}_n$ mean?
It is the set of the first $n$ natural numbers. But please note that different places have different conventions, regarding whether $0$ is included, or whether $n$ is included. In simplicial homotopy ...
- 5,006
4
votes
Accepted
How to write property for every element in a set
(1st paragraph originally a comment)
It would help to explain why you feel that you need to restate this straightforward statement in mathy symbolic form. For instance, are you trying to analyze ...
- 37.6k
3
votes
Accepted
Confusion using function composition
I assume that the confusion is arising in the following line from the linked answer:
Since $h(t)=\sqrt t$, you have $g(t)=\cos(h(t)^2)$, [...]
You are trying to find $g$ as a function of $h$, where ...
- 2,811
3
votes
Accepted
Are $\lim_{(n,m) \to (\infty,x\infty)} (1 + 1/n)^m$ and ${\substack{n \to \infty \\m = nx}} (1 + \frac1n)^m$ correct alternative definitions of $e^x$?
The first option is wrong because $x \infty$ is not well-defined in this context.
The second option is correct, but the notation is non-standard. I would just write:
$$e^x = \lim_{n \to \infty} (1 + 1/...
3
votes
Reading mathematical notation
There does exist a site, Mathjax Speech Converter, that can do this. For example, it will take the following expression (that I randomly made up) "(n + 6)/(n+1)=x\forall n\in R_+" and output ...
- 2,021
3
votes
Accepted
Meaning of the notation $Z_p(G)$
The passage from the book deals with stem groups: in case of isoclinism (an equivalence relation on the class of groups, coarser than isomorphism; isoclinism works better for the classification of $p$-...
- 50.5k
3
votes
Accepted
Simplifying $10^{2380849\cdot 10^{10^{120.20}}-1}$ using Knuth's Up-Arrow notation
This number is not large enough for up-arrow notation to be of much use. It's "essentially" the same as $10^{10^{10^{10^{2.08}}}}$ (the factor of $2380849$ in the first level exponent is ...
- 37.6k
2
votes
Notation for equivalent equations
What is the notation for showing that equations are equivalent after rearranging terms?
For example,
$$s=r\theta\implies r=\frac{s}{\theta}.\tag{✘ 1}$$
Is this the correct way to write it?
Consider ...
- 40.8k
2
votes
Question About the Existential Quantifier, $\exists$
They are dual to each other.
While $∀$ says that $∀x. \varphi(x)$ is true if and only if for all $x$, $\varphi(x)$ is true;
$\exists$ says that $∃x.\ \varphi(x)$ is false if and only if forall $x$, $\...
- 1,469
2
votes
Accepted
Is the interval notation valid for $\mathbb{C}$?
Even if you are doing complex analysis, I think it is fine to write $(0,1)$ to mean $\{x\in\mathbb R\mid 0<x<1\}$. You might want to write "the interval $(0,1$)" if you feel the reader ...
- 21.4k
2
votes
Symbol for a strict implication
First off, the phrase strict implication (usually, denoted by $⥽$) is a specific conditional in logic, different from the one expressed in the question which comes across as considering the statement ’...
- 2,591
2
votes
Symbol for a strict implication
$$P \to Q \wedge \neg (Q \to P) = $$
$$(\neg P \vee Q) \wedge (\neg (\neg Q \vee P)) = $$
$$(\neg P \vee Q) \wedge (Q \wedge \neg P) = $$
$$(\neg P \wedge (Q \wedge \neg P)) \vee (Q \wedge (Q \wedge \...
- 324
1
vote
Accepted
How to denote domain and range of a function that substitutes a given interval?
How about something like:
We write $I_c$ to denote the set of closed intervals $[a,b] \subset \mathbb{R}$ where $a,b \in \mathbb{R}$ and $a \leq b$.
Consider a function $f:I_c \rightarrow I_c$ defined ...
- 15.8k
1
vote
Accepted
Math Operators with Changing Sub-Properties?
This isn't a thing in mathematics.
In math, we use side-effect-free operations. To properly reason about things, any statements about them need to remain true; if we declare that $2\mathrel{Ϡ}2 = 6$, ...
- 2,966
1
vote
Accepted
What is the meaning of "$m$" and "$2$" in "$m \angle GLI = 2 m \angle GLH$"?
The m means the angle is congruent or of having equal length or measure right?
Generally, it does: $m \angle A$ typically means "the measure of angle $A$", and $m \angle ABC$ would mean &...
- 47.5k
1
vote
How is a cone most often (or by convention) notated to show its exact shape?
The circular cone given ( base radius, height) is commonly and fully understood.
Respectively with the above $(r,h)$ are derived slant height slope angle ( generator angle ) a.k.a. the semi vertical ...
- 41.3k
1
vote
What is the meaning of this symbol $\otimes$, in particular for quaternions?
You might be looking for the composition of Euler-Rodrigues symmetric parameters.
They're defined in Shuster 1993, "A Survey of Attitude Representations' see equations (171), (185), (188) etc
$$ \...
- 49
1
vote
How to write property for every element in a set
The colon is perfectly fine. Some books would instead write it as
$$g(v_i)=g(v_j)\ \forall v_i,v_j\in V$$
which may look more "normal" to you. It doesn't really matter as long as it is clear ...
- 8,205
1
vote
Mathematical notation to cap value on 1?
Taking the ideas of @spaceisdarkgreen. Yes, there's a concise and elegant way to express it using the $\min$ function. You can write it as:
$$h(x) = \min(f(x), 1)$$
This notation captures the behavior ...
- 1,320
1
vote
Notation for "the sum of column elements in a in the upper triangle of a matrix for a given row"
You could use the Hadamard product of matrices to get
$$
\pmatrix{1&1&1\\0&1&1\\0&0&1} \odot \pmatrix{a&b&c\\d&e&f\\g&h&k} =
\pmatrix{a&b&c\\0&...
- 41.4k
1
vote
Accepted
Notation for "the sum of column elements in a in the upper triangle of a matrix for a given row"
Well, the standard way to write this would be
$$\text{Upper Row Sum}_i(A) = \sum_{j=i}^n A_{i,j}$$
Are you looking for something more compact than this?
- 2,966
Only top scored, non community-wiki answers of a minimum length are eligible