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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In set theory, what does it mean for a variable to have a bar symbol above it?

Please see the image below. What does the bar symbol mean in this context?
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How do I indicate approximation by rounding when manipulating equations?

I manipulate a set of inequalities and arrive at $$\Leftrightarrow \frac{(||\nu|| - \lambda^{-1})^2}{2\tau^2} \geq 53\ln(2)$$ Note the $\Leftrightarrow$ sign, indicating that this inequality is ...
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Notation for the set of zero divisors in a ring

If $R$ is a nonzero ring with identity then I have seen the group of units denoted by $R^{\times}$ or possibly $R^*$ in some texts. In a classical ring there is a trichotomy which declares each ...
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Can functions be passed into functions and then called?

In computer science there are what are known as higher-order functions. This means pretty much nothing, really. It is a property of a programming language. I want to know if they are valid in ...
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Understanding metric tensor notation

I am trying to understand if there is a conventional way to read super- and subscript notation of metric tensors. Is there a canonical way of doing this? For instance, what is the difference between ...
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$f$ equals <fill in blanks>

Related to: Question about $x\mapsto f(x)$ notation. Is there a way to write $f = \text{some expression}$, and thus define a function without a domain or a variable? A function is too often defined ...
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Describing a function with independent variables.

The normal distribution is often written $f(x\,\rvert\,\mu,\sigma^2)$, with the independent variables on the right side of the vertical line. Is this notation common, or are alternatives? For instance,...
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In mathematics, what is a placeholder?

Google defines the word placeholder in the following image: My question is: Is this the only definition of the word placeholder in mathematics? I am thinking along the lines: If $M = p^k m^2$ ...
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Sampling Distribution Notations

I'm reading a chapter on sampling distributions of a statistic and I don't seem to have an understanding of the notations used. From probability theory, a random variable is usually denoted by a ...
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What are the differences between: $\sqrt{(-3)^2}$, $\sqrt{-3^2}$ and $(\sqrt{-3})^2$. [closed]

First, is $\sqrt{-3}$ is equal to $-3$ or is it imaginary? What is the difference between: $\sqrt{(-3)^2}$ $\sqrt{-3^2}$ $(\sqrt{-3})^2$ Can I write $(\sqrt{-3})^2 = -3$? And, given the rule ...
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Set notation for unordered cartesian product

In the question unordered cartesian product an shorthand notation for the unordered cartesian product was discussed but without any standard notation. So my question is what would be the explicit ...
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What does the '#' sign mean in elliptic curves?

My question is regarding specifically elliptic curves. I have seen the notation $\#E(\mathbb{F}_{q})$ used over and over again (especially in the description of Hasse's theorem). I know that sometimes ...
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Proper notation for motion integration

Say you have a projectile where at $t=0$, $v = 0$ and $x = 0$. Given $\ddot x = -4$, in order to find $\dot x$, we must integrate $\frac{dv}{dt}$ as follows:  \frac{dv}{dt} = -4 \...
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derivative and curl vector notational difference

This must be a really trivial question, and I am not sure I am allowed to post these here. Just wanted to know but didn't know what to search. What is the difference between $\overrightarrow {dr}$ and ...
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What is common notation for “disjoint union of copies of $\mathbb{R}$”?

I'm looking at a question out of Lee's Smooth Manifolds: Show that a disjoint union of uncountably many copies of $\Bbb{R}$ is locally Euclidian and Hausdorff but not second countable. My ...
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How $f:[a,b]\rightarrow[c,d]$ should be read?

I found it in a book but I don't know what the ":" means. What does this expression mean?
Why is $\wedge$ a minimum and $\vee$ a maximum? [closed]
Why does $\wedge$ denote a minimum and $\vee$ a maximum? Where did this notation come from? I keep getting them mixed up because to me, $\wedge$ should be a maximum: it's a hill, or a curve reaching ...
Even if $f:X\to Y$ is not a bijective function, can I still notate the inverse relation of $f$ as $g:Y\to X$?