New answers tagged notation
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Does any recognize this notation which is supposed to be used in former USSR countries?
See this answer. It asserts that in programming the double-slash notation means "ignore the comment following this mark". It is conceivable that similar notation is used in proofreading ...
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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 ...
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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 ...
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How to write property for every element in a set
I've seen a couple of ways in which you can represent statements of the form above.
Statement: "The degree of every vertex in the set V is the same"
$\forall v_i, v_j\in V(g(v_i)=g(v_j))$
$...
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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
$$ \...
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What does $\cos \operatorname{am} $ mean?
It's the Jacobi amplitude. See https://en.wikipedia.org/wiki/Jacobi_elliptic_functions#Definition_in_terms_of_inverses_of_elliptic_integrals
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Symbol for a strict implication
$$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 \...
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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 ’...
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Is it correct to write $f(x,t) = f(x \pm vt)$?
Yes, it is correct, assuming we are working in the context of physics.
From the perspective of pure mathematicians, this notation would be strange for the reason you said; mathematicians work with ...
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Probability Distribution Notation
I used $p(k)$ as $\text{Pr}\{X=k\}$ and followed the hint provided in the textbook to achieve the solution.
Note: for those who don't have a copy of the book, here is the question:
suppose a jar has $...
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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 $p$-...
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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 ...
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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 ...
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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 ...
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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 &...
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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 $e^x$?
Your first option doesn't really make much sense since $x\infty$ is ill-defined. I guess if you interpret it like "$\operatorname{sign}(x) \cdot \infty$" you can salvage that bit of it, ...
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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:
$$e^x = \lim_{n \to \infty} (1 + 1/...
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Question About the Existential Quantifier, $\exists$
They are dual to each other.
While $∀$ says that $∀x. \varphi(x)$ is true if and only if for all $x$, $\varphi(x)$ is true;
$\exists$ says that $∃x.\ \varphi(x)$ is false if and only if forall $x$, $\...
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What does $\mathbb{N}_n$ mean?
It is the set of the first $n$ natural numbers. But please note that different places have different conventions, regarding whether $0$ is included, or whether $n$ is included. In simplicial homotopy ...
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Math Operators with Changing Sub-Properties?
This isn't a thing in mathematics.
In math, we use side-effect-free operations. To properly reason about things, any statements about them need to remain true; if we declare that $2\mathrel{Ϡ}2 = 6$, ...
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Confusion using function composition
I assume that the confusion is arising in the following line from the linked answer:
Since $h(t)=\sqrt t$, you have $g(t)=\cos(h(t)^2)$, [...]
You are trying to find $g$ as a function of $h$, where ...
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Notation for equivalent equations
What is the notation for showing that equations are equivalent after rearranging terms?
For example,
$$s=r\theta\implies r=\frac{s}{\theta}.\tag{✘ 1}$$
Is this the correct way to write it?
Consider ...
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How to denote domain and range of a function that substitutes a given interval?
How about something like:
We write $I_c$ to denote the set of closed intervals $[a,b] \subset \mathbb{R}$ where $a,b \in \mathbb{R}$ and $a \leq b$.
Consider a function $f:I_c \rightarrow I_c$ defined ...
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Why is arcsin represented with the ^(-1) notation?
There is the multiplicative meaning of the exponent (iterated product), and the functional meaning (iterated function composition).
$x^2$ is the square of $x$ or $x\cdot x$, $x^3$ is the cube, $x^{-1}$...
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Does tetration go up or down? (and other related questions)
Tetration is evaluated from the top of the exponent going downwards as mentioned in the Wiki page. (https://en.wikipedia.org/wiki/Tetration)
So, it'd be $2^{65536}$ for your first question.
Usually, ...
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What does this the curly brace mean in an integral
More context would be needed to give a confident answer, but one common instance is that “1” is the characteristic function, meaning it equals 1 inside a relevant domain and 0 everywhere else. In this ...
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Question on notation in Extremal Combinatorics
It's because the larget binomial coefficient is not necessarily unique. For example in the row
$$
1,5,10,10,5,1
$$
the largest coefficient appears twice. That's when you have the duplication in $\...
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Does the Wedge Operator (^) have some meaning in Linear Programming?
The wedge $\land$ is a logical "and" operator; in all cases, it indicates that both (or all) of the given constraints must hold at the same time. For example, when we write the constraint $C$...
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Is an infinite composition of bijections always a bijection?
If you'll forgive me for the digression, here is an answer for the question in your title rather than the one in your body. "Infinite composition", in my experience, tends to refer to the ...
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Does "Doing a thing to both sides of an equation" have a name?
The name for this law in formal logic is "The Indiscernibility of Identities", although usually applied to relations rather than functions.
It says $(x = y) \implies (\forall P ~ P(x) = P(y))...
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