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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Difference between functional notation with parenthesis ommited and 'polish' notation?

Take an example like $-x$, in functional notation this should be $-(x)$, when we actually substitute it, we do include the parenthesis so $-x=-(4)$ when $x=4$, we do this is a lot of cases with unary operators, is it a case of using polish notation…
user37577
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Which statement is correct if I want to combine the given two statements in compact form?

I have these two statements:\ (i). If $A>0$, the left object touches the right object for $B>0$ (ii). If $A<0$, the right object touches the left object for $B<0$ How can I write these statements in a compact form in only one statement? Which one…
sara96
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Set of rational numbers having denominator $D$

The set of rational numbers is customarily denoted $\mathbb{Q}$. I need a symbol for the set of rational numbers having denominator $D$. For example, for $D = 3$, this set would be $$\{ \cdots, -4/3, -3/3, -2/3, -1/3, 0/3, 1/3, 2/3, 3/3, 4/3, \cdots…
Max
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Double arrow between sets meaning?

From C.E. Patrascu and M. Patrascu's "Computing Order Statistics in the Farey Sequence" there is a line: {all fractions in [0, x) with denominator q} ←→ {reduced fractions with denominator d, for all d|q} Note q is an integer, x is real. What is the…
Alex F.
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e-notation scientific notation

Hey all I asked this over at StackOverflow =) and I got a good answer but I still have no idea whats going on. I want to know how the expression got to the answer and maybe the math behind how it was reasoned.. the steps if you would be so kind. The…
BenniMcBeno
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Meaning of the symbol ≡.

I want to know the meaning of ≡ this symbol. I read about it on Wikipedia but didn't actually understand what that means. I saw this symbol in coordinate geometry where it was given that $A \equiv (1,2)$. But what's wrong with $A = (1, 2)$? Is it…
user983440
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What is the convention for listing an uncountable series of elements"

If I have an uncountable series of elements $x_j$, what is the convention for listing them? It doesn't correct to write: $\{x_1, x_2, x_3, \ldots \}$ since that implies they can be indexed by $\mathbb{N}$. Maybe we don't list uncountable elements…
TonyK
  • 403
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Sum of square roots vs. square root of sum in summation notation

Recently, a TA of mine wrote $$ \sum_{i=0}^n \sqrt x_i $$ to represent the sum $$ \sqrt {x_0 + x_1 + \cdots + x_{n-1} + x_n}. $$ Is this an incorrect use of summation notation? My instinct is that the above sum is better represented by the…
steph
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Notation for setting a variable to an equality?

Is there notation for setting a variable equal to the point where some expressions are equal? E.x. $$ c = (\sqrt{x}=2) $$ which becomes $$ c=4 $$ Because $$ \sqrt{4} = 2 $$
b44ken
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What would be the correct notation to define a functional that also uses a scalar variable?

I'm wondering how I should define a functional operator (a map from a space of functions to another space of functions) that also takes in a scalar valued variable as an argument. Question: How should I define an operator $G$ that maps a function…
Mr. President
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why do we tend to use curly braces for the arguments to the min and max functions?

Why is it that we denote the arguments of the min/max functions with curly braces, i.e. $\{$ and $\}$? My first thought would be that it's related to sets and infimum and supremum, but many times it no longer seems to relate to a set, i.e. when used…
trevoryao
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$u \in L^2(R^n)$ what does this mean?

$u \in L^2(R^n)$ I am guessing that $L^2(R^n)$ means the $L^2$ norm over an n-dimensional vector. The context is an energy minimization function : total variation–based model of Rudin, Osher, and Fatemi (ROF)
AnkurVijay
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Typesetting: do you include a space between variables in a formula?

I'm pretty sure this applies to most typesetting languages for math. When entering a formula, do you insert a hard space between symbols? For example, if I have 'a' for acceleration and 't' for time, would I typeset like…
Quark Soup
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Mathematical notation to specify that a variable can reach a max value of $1$ and a min value of $0$

How can I specify within a formula that the inserted values for different variables may only vary between $0$ and $1$? Example: $x = y + z$, where the values used for $y$ and $z$ may take on any value between $0$ and $1$, but not outside this…
john
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Is the notation $[x,\to[$ common?

I recently started reading Topology and Groupoids by Ronald Brown and this notation came up. The notations is $$[x,\to[ \; =\{z \mid x \leq z\}$$ and a similar notation for other type of intervals. I have never seen this before, and I was baffled…
user29123
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