# 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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### Formal representtion of cases in mathematics

Trivial part: Solving a quadratic equation $ax^2 + bx + c = 0$, where $a,b,c$ are real numbers, requires to consider two cases: (i) $a=0$ and (ii) $a \neq 0$. In the first case there is only one ...
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### Is there a name for the logical scenario where A does not necessarily imply B, but B implies A?

A real life example of this is the 'Active' status on Facebook Messenger. (For those interested see this article here, and some Quora answers here for details.) When you are actively using Facebook ...
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### Describing sets from running indices

For a paper I have a set of particles which I usually reference by $p$. The paper is physics related, so I haven't made any real formal definition of the set, and always just relate to them as "the ...
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I'm reading the chapter about perfect sampling of the "Monte Carlo Statistical Methods" by Robert and Casella, 2004. I've got an issue about notation, when they talk about random mappings, they say $$... 3answers 26 views ### Ideal generated by an element Let R\left [ x \right ] denote the set of all polynomials with real coefficients and let A denote the subset of all polynomials with constant term 0. Then A is an ideal of R\left [ x \right ... 1answer 32 views ### Notation: rotation matrix with a condition I'm building a space simulation & am using this resource for converting Keplerian Orbit Elements to Cartesian Co-ordinates. The notation for step 6 has me slightly confused: Is the top part ... 1answer 35 views ### is Cov(X) and Var(X) same? when X is random vector i'm studying with hogg. introduction to mathematical statistics. and i learned about random vector but i wonder whether Cov(X) and Var(X) is same or not. as intuitive thinking , if X is a random ... 1answer 22 views ### Index notation in vector functions Suppose I have a vector \vec u that depends on a vector \vec x and a scalar t, so each component of \vec u depend on all components of \vec x. How can I show this relationship with index ... 2answers 26 views ### Notation for the subset of a set without the last elements I have an ordered set S=\{23,45,32,56\} I would like to make an ordered subset M=\{23,45,32\} which contains the elements of S except the last one. In this case. How do I represent this formally ... 1answer 18 views ### ordered set notation in functions Do please forgive me, if this question is a duplicate. How does one correctly notate a function f, which takes a ordered subset S from the field \mathbb{K} and returns an other (ordered) subset ... 1answer 14 views ### Asymptotic notation basics Say that we have the function$$ 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)$$I'm fairly new to these notations and am ... 1answer 55 views ### What does (0:x) mean? The following excerpt is from Eisenbud's "Commutative Algebra with a view toward Algebraic Geometry" on pg. 424 We can decide whether an element x\in R is a nonzerodivisor from the homology of ... 1answer 39 views ### Question on the Notation of an Abstract Algebra Question The following is a question that I came across in a textbook I'm reviewing for self-study. The book is "Introduction to Abstract Algebra", 4th Edition, by W. Keith Nicholson. I have a question both ... 1answer 25 views ### Concerning the notation \chi (U) in one of the hypothesis for some properties of curl and divergence I have the following exercise: Let U \subset \mathbb{R}^3 be open, X \in \chi (U) and f \in C^{\infty}(U), prove the following:$$curl(\nabla f)=0 \\ div(curl(X))=0 \\ curl(f.X)= f.curl(X)+(\...
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Consider the following two partitions. Partition $\lambda=4^4=(4,4,4,4)$ o o o o o o o o o o o o o o o o And partition $\mu=(4,2,1,0)$ ...
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### $A^\dagger$ - how to handwrite this?!

In one book I came across the notation $A^\dagger := \overline{A}^T$. But how does one usually handwrite it? When I try to do it, it seems so similar to $A^+$
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### Is there a blackboard bold letter for the set of Boolean numbers? [duplicate]

Is there a symbol (e.g. $\mathbb{B}$) for the special set of Boolean numbers or values; ${0,1}$ or ${True,False}$?
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### What is $\mathbb{Z_{n}}\left [ x \right ]$

Question: Show that $\mathbb{Z_{n}}\left [ x \right ]$ has characteristic $n$. What does $\mathbb{Z_{n}}\left [ x \right ]$ stands for? I'm very sure this is not the gaussian ring.
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### Enunciating utility maximization problem using set theory

I need to enunciate a problem using set theory and I am not sure how to start. The problem goes like this: You are a car manufacturer and need to decide how many colours to use in your next bash of ...
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### How does variable ordering in expressions work when creating functions from an equation?

I'm having a really hard time understanding some aspects of functions, i've tried looking around on Khan academy and haven't quite found something to answer my question, i'm sure i'm overlooking ...
I just played around with archimedes $\pi$ formula and ended up with $\pi = \lim\limits_{n \to \infty} 6 \cdot 2^n \cdot \sqrt{2 - \sqrt{2 + \sqrt{2 + ...n times... \sqrt{2 + \sqrt{3}}}}}$ I want to ...