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Mathematics Stack Exchange

Questions tagged [notation]

Questions 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.

Before asking a question on the site, please check if you can find your answer in Earliest Uses of Various Mathematical Symbols or the book A History of Mathematical Notations.

Alternatively, a textbook or paper usually takes the time to explain the notation they're using; please remember to mention where you've seen the notation you are asking about.

12848 questions
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Notation for repeated division

For addition, there is $\sum$ For multiplication, there is $\prod$ What about for division? Something like ${/}_{i=1}^n a_i = a_1 \div a_2\ \div\ ...\ \div\ a_n$?
Nick
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greater than and NOT equal to

I have two vectors, $x, y\in \mathbb{R}^N$ with $N>1$. Consider an order such that $x\geq y$ iff $x_i\geq y_i$ for each $i=1,2,\ldots, N$, and $x> y$ iff $x_i> y_i$ for each $i=1,2,\ldots, N$. I want to highlight the fact that (a) $x\geq y$, (b)…
tsm
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Represent number of value repeats after decimal

Is there a way to represent the number of times a value has repeated after a decimal point? For example if I have: 0.9 0.99 0.999 Is there something like: 9E-1 9E-2 9E-3 That easily represents these values?
The Nightman
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Countable and uncountable Cartesian product

We can recursively define a tuple: \begin{align*} \langle x \rangle &= x\\ \langle x_1,\ldots,x_{n+1} \rangle &= \langle \langle x_1,\ldots,x_{n}\rangle, x_{n+1}\rangle \\ \end{align*} We can define functions as sets of tuples $\langle x,y…
antonio
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What does "$\|$" mean in a statement such as $d<\|r-s\|$?

Recently, I saw a math equation on GameDev.SE with $\|$ in it, and I was confused because this was new to me. I googled it, but being a symbol, nothing specifically on it came up in my results. The equation is supposed to find if a circle…
Plqsmic
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What's the notation for odd integers modulo their powers of $2$?

We have of course: $2\Bbb Z-1$, or $2\Bbb N+1$ These I think of as the integers reduced by the congruence $x\cong x+1$ where in one case $x$ is even and in the other $x$ is odd (it makes no difference really). But I want to think specifically of…
it's a hire car baby
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What does "$ℝ^{4\times10}$" mean

I was given this statement: where $W\in\mathbb R^{4\times 10}$ and $\vec{b}\in\mathbb R^4$. Now, I understand that $ℝ^{4}$ means that the set of real numbers in four dimensions. However, I am not sure what $ℝ^{4\times10}$ mean?
Pablo
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Notation of several functions defined identiaclly

One can consider the following functions: $$f(x):X\mapsto{R}$$ $$g(x):X\mapsto{R}$$ $$h(x):X\mapsto{R}$$ Is it correct to rewrite above mentioned in the following way: $$f,g,h:X\mapsto{R}$$ or what is the appropriate way to rewrite aforementioned in…
David
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How do you write a vector clearly on one line?

I've learned to write a vector on one line as for example $(a,b,c)$. This can get very confusing if each component of the vector is an expression of several terms like this: $(a+b,b+c,a+b)$ since the commas get mixed up in the mess of signs. Adding…
dekuShrub
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What does $t\in [0, N )$ mean?

I know it means that t is an element in the range from 0 to all natural numbers (I think) but what do the [ and ) represent?
Adjit
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Unclear Notation in a "PDE"

In our problem sheet on Real Analysis, there is a problem that seems to be unprecise (perhaps it's just me - I'm sorry if that's the case.). I'm asking you to please only answer on what the notation should say (and not spoil anything on the…
Qi Zhu
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Notation question, $x=1,2,3...$ or $x\in \mathbb N$?

On my recent exam, my professor wrote a note saying that the following notation shouldn't be used when discussing domains, and I'm not sure why it matters. So, my question: I'll use a specific example, but I'm speaking generally when it comes to…
NoVa
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Meaning of following notation

I came across the following notation used for a function $f$: $$|f|_{L^\infty}$$ What does this notation denote?
john doe
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How to denote an arbitrary expression involving some number of dummy variables?

Let me give you an example. $(n)_{n=0}^{\infty}$ is a reference to a particular Sequence object. $$ 0, 1, 2, \ldots $$ Is another way to reference the same sequence object. $a_n = n\forall n\in \mathbb{N}$, $(a_n)_{n=0}^{\infty}$ is yet another way…
extremeaxe5
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What does the notation $h \ll 1$ mean?

The following screenshot is taken from some lecture notes on actuarial mathematics: As you can see, the notation $h \ll 1$ is used here (in the first line of the proof). Does anyone know what this is supposed to denote? I first suspected that it…
M Smith
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