Mathematics Stack Exchange
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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Is my use of $\pm/\mp$ in answers allowed notation?

If we solve the equations: $$x^3+2x^2-9x+2 = 0\\\therefore x = 3, -3, -2\\\therefore x = \pm3, -2$$ $$x^3-4 x^2+9 x-10\\\therefore x = 1+2i, 1-2i, 2\\\therefore x = 1\pm 2i, 2$$ It seems to me that $x = 1 \pm 2i, 2$ would fit better, as we know that…
user164476
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A question on function notation

Forgive me if this does not belong here. All throughout primary school I've seen the notation $f(x)$ to denote a function, that is, if we are talking about the squaring function, we would write $$ f(x) = x^2 $$ to denote/define the function (IIRC…
gardenhead
  • 253
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Is there standard notation for an arbitrary polynomial of degree $k$?

I was wondering whether there is standard notation for a polynomial of a certain degree, say, $k$. That is, I want to be able to write $ $ instead of "..., where $p(x)$ is a polynomial of degree $k$." Does such a thing…
Ryker
  • 1,499
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I'm confused: does # mean Q.E.D. or contradiction?

Last week one teacher used the pound sign # for implying that we were done proving something and a different teacher used the same for highlighting a contradiction.
Lenar Hoyt
  • 1,062
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4 answers

Symbol for rational/irrational part of a number

Just as $\Im(z)$ and $\Re(z)$ denote the imaginary and real parts of $z$, respectively, do there exist symbols for the rational and irrational parts of a real number?
beep-boop
  • 11,595
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What does the symbol $\mathbb{R}(\zeta)$ denote?

I know hat $\mathbb{R}[\zeta]$ denotes the ring of polynomials in $\zeta$ with real coefficients. I came across the symbol $\mathbb{R}(\zeta)$. Which ring is this?
user144410
  • 1,312
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What's the meaning of $x \choose y$ in the Catalan number formula?

What's the meaning of $\choose$ in this formula: $$C_n=\frac1{n+1}\binom{2n}{n}=\frac{(2n)!}{n!(n+1)!}\qquad\mathrm{for}\;n\geq 0$$ Is it a division?
jiun
  • 211
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4 answers

What does $\exp(f)$ mean?

In several posts around this site, I have encountered the expression $\exp(x)$ where $x$ is an arbitrary expression. What does this notation mean?
Aidan F. Pierce
  • 1,465
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Why is scientific notation of the form a.bcd×10^n?

More specifically, my question is why is the point always after the first digit? Why have (for example), 7.5 x 1018 as opposed to 75 x 1017? The former makes it easier to read (when you literally want to say the number of zeros) in cases where n is…
user137369
  • 133
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Why notations of numbers in standard positional numeral systems when evaluated, evaluates to decimal notation?

For a positional numeral system of radix b, evaluating a notation $a_3 a_2 a_1 a_0$ as shown below results in decimal notation of number, $a_3 a_2 a_1 a_0 = a_3 \times b^3 + a_2 \times b^2 + a_1 \times b^1 + a_0 \times b^0$ Why? PS: Please keep…
iSeeU
  • 31
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Is there any shorthand notation for linear interpolation?

It is quite common for me to encounter or manipulate expressions of the form $$ x + \alpha(y-x) $$ or equivalently $$ (1 - \alpha) x + \alpha y $$ where any of the expressions ($\alpha, x, y$) may be rather complicated. I am not happy with…
dfan
  • 677
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2 answers

Notation when evaluating an integral at infinity

Using a trivial example to illustrate the question - $$\int_0^\infty 2 dx$$ $=2x \mid_0^\infty = 2(\infty) - 2(0)$ Can we actually say $2(\infty)$? It doesn't seem valid me.
csss
  • 3,655
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Questions about notation $\forall$ and $\exists$

I had a few questions about notation $\forall$ and $\exists$. I am posing each of the question for the former, but I have the corresponding question for the latter as well: 1) If I have only one object to quantify, is it more common to write…
B M
  • 930
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Which side should the "hat" of unit vectors point to?

I'm not sure whether to post this here or on TeX.SE. If it belongs there, please move it. When working with unit vectors in physics class, we usually write them with an upside down hat, like this: $\check{\imath}\, \check{\jmath} \,\check{\rho}$.…
Javier
  • 7,298
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why the square root of x equals x to the one half power

Could someone explain how/why the square root of $x$ equals $x$ to the one half power? I know by definition it does, but is there any mathematical process we can go through to get from one to the other? In addition, I know the $x$ to the 2ed power…
user1404617
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