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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When writing $f\colon X \rightarrow Y$, which set $Y$ should one specify?

Consider a function introduced by $f \colon X \rightarrow Y$. While $X$ is the domain of the function, my understanding is that $Y$ is the codomain -- and not the image! However, there are many possible codomains which one can specify. Is the…
afreelunch
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What notation is used for rings with two alternative multiplications?

Suppose one has a ring with two alternative multiplications, like "$\times$" and "$\cdot$". Each one rises a set of analytic functions that can be applied to the elements of the ring. What notations are used to differentiate between functions built…
Anixx
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Is there a notation that allows me to refer to the first/second element of an ordered pair?

In programming, we define an "array" (basically an ordered n-tuple) in the following way: $$a=[3,5].$$ Later on, if we want to refer to the first element of the predetermined array/pair/n-tuple, we write $a[0]$ (because in programming you start…
Dark Rebellion
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Is the smallest field of a finite set also denoted $\sigma$(.)?

The collection $\{A, A^c, \emptyset, \Omega\}$ is, I think, the smallest field generated by A. Is this also denoted $\sigma$(A) or is that notation reserved for $\sigma$-fields?
TonyK
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What does this symbol "‰" mean in metabolic studies.

Have a look at this article and you can understand the research area. Jahren, A.H., Kraft, R.A., 2008. Carbon and nitrogen stable isotopes in fast food: Signatures of corn and confinement. Proceedings of the National Academy of Sciences 105,…
Barry Marshall
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Better notation than "$(\cdot)$" for an arbitrary symbol?

Say I want to make clear that, say, the index $i$ on a symbol always means "initial configuration", or the "hat" $\hat{}$ always stands for "maximum". What I've seen a couple times is the notation bracket \cdot bracket, as in "$(\cdot)_i$ means the…
MaxD
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Is it possible to use a variable as an operator?

This is more of a notation question, but is there a (correct) way to use an operator as a variable? Like this perhaps$$\text{let H be} <$$ or $$H:<$$ Where $H$ is now equivalent to $<$
MarkW
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How to write $a=b\Leftrightarrow c=d\Leftrightarrow e=f$ is the expression does not fit a single line?

I am currently showing that $a=b\Leftrightarrow e=f$ by showing that $a=b\Leftrightarrow c=d\Leftrightarrow e=f$. The problem that I have is that the expressions $\{a,b,c,d,e,f\}$ are rather long and do not fit in a single line. I am currently…
EoDmnFOr3q
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Is there a symbol for "cannot equal to"?

I know $\overset{!}{=}$ means "must be equal to." Would it be reasonable to conclude that $\overset{!}{\neq}$ means "must be equal to anything but", i.e. "cannot equal to"? References: Notation for “should be equal to” Must be equal and other…
GPWR
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Index position of a tensor

A vector field $V$ is in P; that is $V^c $ if we considere $x^c$, $V^b$ if we consider $x^b$. $\nabla_b V^c$ means that we evaluate the variation of $V$ components in passing from $x^c$ to $x^b$ (and it isn't a tensor) The "rate of change" is…
Andrew
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Parentheses for $\displaystyle\sum_{i=1}^n x_i \prod_{j=1}^i(y_j + \alpha)$

I am typesetting an equation of the form $$\sum_{i=1}^n\Bigl(x_i \prod_{j=1}^i(y_j + \alpha) \Bigr)$$ Originally, I wrote the equation without the outer pair of parentheses, and a reviewer asked me to include them. I agree that they improve the…
Max
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Notation for set-valued function that returns a non-fixed set length

Sorry if it seems a silly question. I have a function $f$ that returns a certain set of elements that are all in the same domain. The exact number of element depends on the input. For example $f(x) = \{0,1\}$ for $x = 42$ and $f(x) = \{0,1,2\}$ for…
Welgriv
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Is it a common or accepted practice to specify measurement units directly in the formula?

Is it a common or accepted practice to specify measurement units directly in the formula? Something like where X is given in miles, Y in kilometers, and Z in millimeters.
john c. j.
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$+x = x$ (A mathematical convention?)

It seems to me that, by convention, the equality $+x = x$ holds for any real (or complex) number $x$. I have not, however, found such a convention explicitly presented in any text. Well... am I wrong and there is no such convention?
Paulo Argolo
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Notation for set of maps.

The set of all homomorphisms between two spaces $X$ and $Y$ is denoted as $\text{Hom}(X,Y)$, the set of endomorphisms of a space $X$ is denoted as $\text{End}(X)$,... these are standard notations, but what about the set of all maps between two…
Marcos
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