# Tagged Questions

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.

26 views

### Does the Statement $\lim_{f(x)\to a}k(x)$ Make Sense

In a formal mathematics context does the statement $$\lim_{f(x)\to a}k(x)$$ where $f(x)\neq c$, where $c$ is a constant, make sense? For example does $$\lim_{x^2\to 0}x$$ make any sense in a formal ...
1k views

### Are there dictionaries in math?

Consider the following dictionary in the programming language Python: D = {'A': 1, 'B': 2, 'C': 3} It is saying that the value of A is 1, the value of B is 2, ...
28 views

25 views

### Notation check, argmax of values in a set [on hold]

Among C different possible values for each y and m total ...
60 views

35 views

268 views

### Difference between | and / [duplicate]

"If we find a prime $p$ such that $p\mid n$ , then $n/p$ is a positive integer that's smaller than $n$." I understand $n/p$ is $n$ divided by $p$ but what is $n\mid p$?
30 views

### How to show continuity of a function with $n-1$ exponentiations?

Say we are given a function $$\Gamma(x)=f_1(x)^{f_2(x)^{\cdot^{\cdot^{f_n(x)}}}}$$ where $f_i,i\in[1;n]$, are continuous functions in their domains. Also assume that the function makes sense, e.g., ...
42 views

Why is, for the modulus operation, the notation $A\equiv C \pmod B$ used instead of $A \text{ mod } B = C$? Or alternatively $\text{mod}(A,B) = C$ or, as in many programming languages, $A\text{ } \% \... 0answers 9 views ### Is this correct for an explicit represenation of the$\Vert f \Vert_{C^2(\mathbb{R}^2)}$norm that uses multi-index notation? I'm not familiar with multi-index notation so I'm not sure if I have this correct. Say we have (taken from here) $$\Vert f \Vert_{C^2(\mathbb{R}^2)} = \sum_{j=0}^2 \sup_{x \in \mathbb{R}^2} |\nabla^j ... 0answers 14 views ### Function notation ?? From the Euler-Lagrange equation$$ I(\alpha) = \int_{x_1}^{x_2}F(Y,Y',x)dx  \frac{dI}{d\alpha} = \int_{x_1}^{x_2}[\frac{\partial F}{\partial Y}\frac{\partial Y}{d\alpha}+\frac{\partial F}{\... 1answer 32 views ### Simple set-builder notation for counting pairs Today I was curious about writing a simple expression using set-builder notation. The expression is the number of integer pairs$(a, b)$such that$a \mid n$,$b \mid n$, and$a \mid b$. My attempt is ... 2answers 46 views ### How do I write$B = \left\{\left[\begin{smallmatrix} x \\ y \end{smallmatrix}\right] \in \boxed{?}| \ldots\right\}$with proper notation Let$x \in X \subset \mathbb{R}^n$, then I define a set: $$A = \{x \in X| 1^Tx = 0\}$$ Now supose I have another element$y \in Y \subset \mathbb{R}^n_{+}$I concatenate$x,y$in to a single vector ... 6answers 11k views ### What did Alan Turing mean when he said he didn't fully understand dy/dx? Alan Turing's notebook has recently been sold at an auction house in London. In it he says this: Written out: The Leibniz notation$\frac{\mathrm{d}y}{\mathrm{d}x}$I find extremely difficult ... 4answers 82 views ###$E(X)$versus$E(X|Y)$Why is$E(X)$considered a constant but$E(X|Y)$considered a random variable? Seems like confusing notation since I'd assume the latter is a fixed constant "the expected value of random variable$X$... 0answers 56 views ### Double integral,$dx$before the integral sign Suppose we have$f(x)g(x,y)$, In some books (Rudin Real and Complex Analysis) the double integral is written as $$\int_X f(x) dx \int_Y g(x,y) dy$$ instead of $$\int_X \int_Y f(x) g(x,y) dy dx.$$ If ... 1answer 33 views ### Hartshorne: Definition of$K^*$where$K$a function field of scheme. Let$X$be a noetherian integral separated scheme which is regular of codimension one. Let$K$be the function field of$X$. Now let$f \in K^*$, (I am interpreting$K^*$to be the set of field ... 1answer 50 views ### Is there a meaning to the notation “\arg \sup”? When$f$is a function on a set$A$, the notation:$\arg\max_{x\in A} f(x)$denotes the set of elements of$A$for which$f$attains its maximum value. This set may be empty, for example, if$f(x)=x$... 2answers 44 views ### Given the function$f:[0,1]→[0,1]$;$f(x)=x^2$, check which one(s) of the properties it has. This homework is past due, but I am still fiddling trying to figure this out. question: I do not understand what the heck the notation of$f:[0,1] \to [0,1]$; means. I thought I did, but my ... 0answers 19 views ### Notation of maximization in pseudocode I'm working on the implementation of a simple algorithm. See this small excerpt: S is a set of points from which I have to choose point p. I am confused as how to find p. I know how to calculate ... 1answer 31 views ### set notation for vectors of unequal elements I am looking for a compact way to represent a group of vectors for which each vector contains no two elements that are the same. $$\textbf{y} \in R^n \quad | \quad y_i \neq y_j \quad \forall \quad ... 3answers 32 views ### Converting from standard to functional, Polish and Reverse Polish notation I wanted to convert the following expression to Functional, Polish and Reverse Polish notation.$$Y =A + \frac{B+ \dfrac{BA}{B+CA}}{A - \dfrac{BC}{B-C+A}}$$I know how to do Standard -> Functional ->... 2answers 18k views ### What are the common abbreviation for minimum in equations? I'm searching for some symbol representing minimum that is commonly used in math equations. 2answers 74 views ### If \lim a_n does not exist, then does this mean that \lim a_n\neq 0? If \displaystyle\lim_{n\to\infty} a_n does not exist or if \displaystyle\lim_{n\to\infty}a_n\neq0, then the series \displaystyle\sum_{n=1}^{\infty} a_n is divergent. From Stewart's Early ... 2answers 36 views ### Notation of the square (or other power) of a function f(x) How do you notate the square (or other power) of a function f(x)? Is it f^2(x) (similar to \sin^2(x) for example), f(x)^2 or do you have to use (f(x))^2? Thanks in advance. 2answers 196 views ### ⋇ “Division Times” operator in Unicode (U+22C7)? [duplicate] I found this maths operator in Unicode: ⋇ It is called "Division Times" (U+22C7). Does it behave like ±? For example: 3 ± 2 means it is an ∈ {1, 5}. So 3 ⋇ 2 means it is an ∈ {1.5, 6}? 0answers 22 views ### Notation for subring of quotient ring Let S be a subring and I an ideal of the ring R. Is there some standard notation for the subring of R/I given by \{ s + I: s \in S \}. Is it appropriate to write S/I even though I is not ... 1answer 425 views ### Element of a sequence notation I'm writing some equations dealing with sets and sequences. I have a sequence S and want to show that x is an element of S, however I am hesitant writing x \in S because I don't want to ... 1answer 104 views ### Why isn't it mathematically rigorous to treat dx's and dy's as variables? [duplicate] If I do something like:$$\frac{dy}{dx} = Ddy = D \times dx$$People would often say that it is not rigorous to do so. But if we start from the definition of the derivative:$$\lim_{h \to ... 1answer 62 views ### Question about the notation$X/A$in topology In Hatcher, the notation$X/A$as appearing in the following text is never defined: If$(X,A)$is a CW Pair consisting of a cell complex$X$and a subcomplex$A$, then the quotient space$X/A$... 0answers 36 views ### notation: meaning of$\frac{dB}{dr}$I'm wondering what$\frac{dB}{dr}$could be? Is it a common notation for$\mid\vec\nabla B\mid$? This would the only thing that would make sense for me! (Occurrence in a text about some physics 'in ... 1answer 35 views ### Summation Notation (Discrete Mathematics) [closed] I am currently studying sequence which I think will lead up to my next topic induction. My question is if$$\sum_{k=0}^n \frac{k+1}{n+k}= \frac{1}{n}+\frac{2}{n+1}+\frac{3}{n+2}+\cdots+\frac{n+1}{2n}$...
Related to $f$ equals <fill in blanks> Is there a way to write a "function" (without lambda calculus) without a domain? For instance, when differentiating, one often just considers $x^3$ as a "...
In the text Linear algebra (Hoffman), there are notations S, Z, M. What are these short for -- that is, why are these particular three letters used for the following concepts? (i) S. Let $W$ ...