# 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.

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### ordered set notation in functions

Do please forgive me, if this question is a duplicate. How does one correctly notate a function $f$, which takes a ordered subset $S$ from the field $\mathbb{K}$ and returns an other (ordered) subset ...
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### Asymptotic notation basics

Say that we have the function $$f(n)=kn, \, k>0$$ does that imply the following? $$f(n) \in O(n), \, f(n) \in \Theta(n) \text{ and } f(n) \in \Omega(n)$$ I'm fairly new to these notations and am ...
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### What does $(0:x)$ mean?

The following excerpt is from Eisenbud's "Commutative Algebra with a view toward Algebraic Geometry" on pg. 424 We can decide whether an element $x\in R$ is a nonzerodivisor from the homology of ...
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### Question on the Notation of an Abstract Algebra Question

The following is a question that I came across in a textbook I'm reviewing for self-study. The book is "Introduction to Abstract Algebra", 4th Edition, by W. Keith Nicholson. I have a question both ...
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### What does the middle dot in parentheses mean?

The below picture is from section 3.3.1 in this paper; I'm not familiar with the notation of using middle dots in square parenthesis. Are the authors using this simply to indicate that any two ...
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### Nested conditional function

I have a number of equations that I am solving in steps so that the answer to preceeding steps affects the answer to the current and future steps. This leads to a number of conditional functions, but ...
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### Gröbner basis is not a vector basis?

We use the same notation for Gröbner basis and vector basis. I recall that $\langle 1\rangle_{GR}$ is the largest Gröbner basis while $\langle 1\rangle_{vector}$ is the smallest vector basis. So for ...
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### Basis of all real polynomials?

I am studying the book Topics in Algebraic Graph Theory by Beineke et all and the page 12. By the book, the set of all real polynomials can be generated by the set $\{1,x,x^2,\ldots\}$ which I ...
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### Why does (h,k) generally represent the center of a circle?

Why are h and k generally used to denote the coordinates of the center of a circle? After a bit of research, we found that h may represent "horizontal shift" or "horizontal translation", but we're ...
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### A little help on mathematical notation and on the definition of a manifold

I was going through the mathematical definition of manifold and it defined it as follow : " A topological space, $\ M$ is an n-dimensional real manifold if there is a family of subsets $\ U _\alpha$...
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### Is there a sign for 'not less than', 'not greater than', etc.?

I was wondering about this, just now, because I was trying to write something like: $880$ is not greater than $950$. I am wondering this because there is a 'not equal to': $\not=$ Not equal to is an ...
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### The notation of 'greater than or equal to'.

I've known that the following marks are equal. However, both marks are used in the same book. I was wondering whether there is some difference between them.
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### Why “deformation retracts to” instead of “deformationally retracts to”?

First, correct me if I'm wrong: I grammatically understand "X deformation retracts to Y" as "X(subject) deformation(adverbial) retracts to(verb) Y(object)". But I just don't understand why we don't ...
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### Why the separate notation for norm

One usually denotes the norm as $\|\cdot\|$, $\| v\| := \sqrt{\langle v, v \rangle}.$ However, in metric spaces, one often writes $d(x,y) \equiv \lvert x-y \rvert$. Since the norm canonically ...
### What does this notation mean? $∂df^2 / ∂x$
I am given variance $\sigma_x$ and function $y=f(x)$ According to my book, the following equation gives the new variance of $y=f(x)$. But I'm not sure what this notation means, as in what this ...