Questions tagged [notation]
For questions about the history and development of how symbols and related objects are written.
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Who first referred to the number of nonzero entries of a vector as its $\ell_0$ norm?
It is common in the compressed sensing literature to refer to the number of nonzero entries of a vector as its $\ell_0$ "norm." The scare quotes are there because strictly speaking, the $\...
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is the shape of the Greek letter pi inspired in the Lion's Gate at Mycenae? [closed]
some references put that the shape of the Greek letter pi is inspired in the lion's gate at Mycenae:
The Symbolism of the Greek Alphabet" by Thomas Taylor(1833)
"The Secret Life of Symbols&...
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Use of blackboard bold "ℝ" to refer to real numbers?
I was looking at Wikipedia's wonderful table of the history of certain mathematical symbols, and there was a certain glaring omission: the use of ℝ to apply to the set of all real numbers. They have ...
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History behind Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$ for a commutative Noetherian ring
In 033Q we find defined what some sources call “Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$” (if you don't know what a scheme is, you can read the definition for a commutative Noetherian ring ...
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Origin of $V_a$ (median) notation
My question about median of a triangle.
The English equivalent of the Turkish word "kenarortay" is "median". In English-language geometry sources (like books or web pages), the ...
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First use of ~ and ≍ (\sym and \asymp)
The relations ~ and ≍ are frequently used in math and computer science, at least within number theory and analysis of algorithms. What is their origin?
Definitions
Suppose $g(x)$ is an eventually-...
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Where does the "operator to the right" notation originate?
If any of you have ever written code in DirectX, you're sure to have noticed that applying a linear operator $A$ to a vector $x$ is done as $xA$, instead of the (nowadays usual) $Ax$. I wanted to know ...
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First time equilibrium notation was used
I was wondering when was the first time that a chemist wrote a chemical equilibrium with the $\rightleftharpoons$ symbol. And if it was before or after Arrhenius's dissociation theory.
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How did Isaac Newton write the integral symbol?
Isaac Newton is known as the discoverer of the FTC (Fundamental Theorem of Calculus), so maybe he wrote the integral symbol and derivative symbol. I know he wrote the derivative symbol as $\dot y$ but ...
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Origin of the usage of $\lambda$ to represent eigenvalues
I'm curious whether anyone knows how $\lambda$ came to be used to represent eigenvalues and or who (if anyone) was responsible for the convention. I've looked through a couple of books on the history ...
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Where did the index of a subgroup notation $[G:H]$ begin to be used?
In texts of algebra, the cardinality of cosets is written in $[G:H]$ or $|G:H|$. Where did this notation originate?
The history about $G/H$ can be found here. $[G:H]$ is called index of a subgroup. ...
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Gate 44 at the Colosseum in Rome: XLIIII or XLIV? When and why the change?
We teach our children in school that 4 is written in Roman numerals as IV and not as IIII but at the Colosseum in Rome, gate 44 is identified as XLIIII and not as XLIV.
When did the change from IIII ...
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Why is 'total angular momentum' denoted by the letter $J$ in quantum mechanics?
In quantum mechanics, we say $J$ ('total angular momentum') = $L$ ('orbital angular momentum') + $S$ ('spin angular momentum').
Apparently $S$ is from 'Spin', but why $J$ for the total angular ...
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Why have advocates for positional number systems based on divisibility favoured base 12?
In the early twentieth century, with Esperanto and the like going on, a small movement called "dozenalism" began, with the aim of replacing base 10 with the purportedly more natural base 12. ...
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Who introduced the mixed fraction notation?
Who introduced mixed fraction notation? This notion is a source of confusion to me because it may be interpreted as multiplication.
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First use of corner quotes for Gödel numbers
Who first used the corner quotes, ⌜ and ⌝, or $\texttt{\Godelnum}$ with Sam Buss's macro, for the notion of Gödel number?
Quine introduced corner quotes, but did not use them for the notion of Gödel ...
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What is the S notation in Student's The Probable Error of a Mean?
In William S. Gosset's The Probable Error of a Mean (JSTOR), he begins to derive the $t$ sampling distribution as follows.
Samples of $n$ individuals are drawn out of a population distributed ...
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Greater-than symbol in Byrne's *The Elements of Euclid*
I was surprised to find that Oliver Byrne's 1847 marvelous The Elements of Euclid (color version)1 uses $\sqsubset$ to mean "greater than" and $\sqsupset$ to mean "less than,"
in ...
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History of italicising variables and mathematical formatting in general
In the modern day, especially with the advent of $\mathrm\TeX$, it is common practice to italicise variables. This can be seen as far back as Hann, J. (1850). Examples on the Integral Calculus. What's ...
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Why isn't the symbol for Beryllium 'B' rather than 'Be'?
What I have understood is, generally the symbol of an element is kept as the first letter of the element's name itself (H, N, O...) unless there's already a symbol with that letter, in that case, we ...
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Why is $T_{\mu\nu}$ the Standard Notation for the Stress-Energy-Momentum Tensor
My question is simple: why do we use $T_{\mu\nu}$ to denote the stress energy momentum tensor, and when was the concept of the stress energy tensor first (or roughly the first) introduced (and by whom)...
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First use of "Spur" (trace) for linear maps / matrices
Every student of linear algebra learns about the trace of a linear map. Its easiest (albeit not most conceptual) definition is: write the map as matrix, then the trace is the sum of the diagonal ...
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Why are the symbols E, F, G, L, M, and N used for the coefficients of the fundamental forms?
In differential geometry, if $e_1$ and $e_2$ are bases for a tangent space $T_pM$, then the coefficients of the first fundamental form is:
$$\begin{align}E&:=\left<e_1,e_1\right>\\F&:=\...
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What is the earliest use of the $\perp\!\!\!\!\perp$ symbol in statistics to denote statistical independence?
The symbol $\perp\!\!\!\!\perp$ in statistics is a way to denote statistical independence of a collection of random variables. I have seen two forms of it. The first is highly suitable in writing ...
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Where does the abomination that is probability notation come from? [closed]
Those with experience may deny it, having suffered too long ago. But it stares you in the face with the somnolent, expressionless eyes of every student being exposed the first time. Probability ...
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Why is electric potential denoted by $\phi$?
I haven't found any explanation for it, and I'm curious.
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Why is the ring of algebraic integers denoted by $\mathcal O_K$?
Why/when was the curly-O notation chosen for the ring of integers of an algebraic number field $K$?
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Question from Whiteside V. 1 - what did Newton mean by a:b :: c:d notation?
I'm reading volume 1 of Whiteside's 'Mathematical Papers of Isaac Newton,' and on pp. 383-384, Newton reaches a conclusion on his "Example 1st" in the statement "55:-54 :: p:q..." -...
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Origin of the special Finnish notation for difference of antiderivative
Apologies for a question that is specific to one country (but perhaps others find it a curious example of how mathematical notation can vary between countries).
In Finnish calculus texts, if $F$ is an ...
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Why is this notation used to define points in (elementary) analytic geometry?
I have always found strange that in elementary analytic geometry points are defined by their names followed by their coordinates, for example:
"Find the distance between $A(5, -3)$ and $B(2, 1)$....
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How has $\tan(x)$ become more popular than $\operatorname{tg}(x)$?
I know that some Eastern European and Middle Asian countries denote the tangent by $\operatorname{tg}$. For many years, I have used $\tan$ instead, but am currently thinking of changing that notation ...
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Why is “h” used for height? [closed]
In Mathematics, it is common to use $h$ for height in various languages, including those whose word for height does not start with h. Why is that?
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The exclamation mark over a relation symbol
My old linear-algebra teacher, whom I can no longer ask, wrote on a black board an exclamation mark over the binary symbol of a logical formula, the main symbol of which is that binary symbol, to say ...
user14234
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Notations for Laplacian: $\nabla^2$ vs. $\Delta$
For a (sufficiently smooth) function $f\colon \Bbb R^n\to\Bbb R$, the Laplacian of $f$ is defined to be $\sum_{j=1}^n \frac{\partial^2 f}{\partial x_j^2}$. There are two notations for the Laplacian ...
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When did contemporary practices for indicating ecliptic longitude supplant those containing zodiacal signs?
Ecliptic longitude may be expressed in degrees; my understanding is that prior to the 19th century, expressions of ecliptic longitude contained zodiacal signs. What contemporaneous accounts describe ...
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Usage of postfix notation for quantifiers
All the logical notations I've seen, from the Begriffschrift notation on, place quantifiers before the proposition containing the variables the quantifier binds. For example, in modern notation we ...
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Reverse subtraction: has any culture had a symbol (call it $\oplus$) where $A \oplus B$ (read in the same direction as in the language) $:= B - A$?
The standard use of the minus sign is such that $A-B$ means you subtract B from A. Thus $$5-2 = 3.$$ Has any culture used a symbol (let's call it $\oplus$) where $A \oplus B$ means you subtract A from ...
user13571
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When was the first recorded use of subscript in mathematics to represent index?
(Disclaimer: apologies for any incorrect usage of mathematical terminology throughout this question.)
In modern mathematical notation, a variable with a subscript can represent a couple of different ...
thBeam
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Origin of Q for the set of rational numbers?
It seems many sources$^1$ attribute the use of the letter "Q" to represent the rationals to the N. Bourbaki group (in the 1930's); however, the Wikipedia entry on rational numbers claims ...
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Origin / first use of $\mathbb{Z}$ (blackboard bold Z)?
I'm aware that the choice of "Z" comes from German zahlen (for "numbers"); however, I was curious to know when the dedicated font, which I believe is called "blackboard bold&...
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Why is there no notation for tetration similar to summation?
I noticed that we use $\sum$ and $\prod$ for summation and infinite product (I don't know why it does not have a name like the other two), but we use different looking notation for tetration. Is there ...
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Notation for the "binomial form" of a polynomial
In Hardy's A Course of Pure Mathematics (§117 in the 10th edition), in a discussion of differentiation of polynomials, he introduces what he calls the "binomial form" of a polynomial:
$$
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Origin of the notation $s = \sigma + j\omega$ in electrical engineering/control theory
In analytic number theory it is traditional to write a complex variable as $s = \sigma + it$, with the letter $t$ going back to Riemann's paper on the zeta-function (1859) and the letter $\sigma$ ...
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What is the origin of the "Japanese bracket"?
In discussions of Sobolev spaces one often sees the Japanese bracket, $$\langle x \rangle = (1+|x|^2)^{1/2},$$ as useful shorthand.
I was not easily able to find information about this term.
(1) What ...
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When did physicists begin using the symbol $G$ for Newton's gravitational constant?
The Cavendish experiment was equivalent to measuring $G,$ Newton's gravitational constant. However, because physicists at the time did not write equations in the same way we do now, Cavendish didn't ...
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How long have parenthesis (brackets) been used?
If you look at a work such as Bertrand Russel's Principia Mathematica there are no brackets at all. So are brackets a recent invention?
Newton used to draw a line above long expressions to group terms....
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How old are the shape of the numbers based on the number of angles?
There is a famous image that pretends to explain the origin of the shapes of the digits by the number of angles in them.
I do know that it is erroneous but I would like to know if this is an old ...
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Why are there so many different, and widely accepted, notational systems for boolean logic?
I can write out the following CNF in various different ways:
In mathematical textbook notation:
$(A \land B \land C) \lor (\lnot A \land B \land \lnot C) $
In C-like programming notation:
...
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What symbols have been used for "many" (or "a large amount of") or "a few" (or "a small amount of") in the history of mathematics or other fields?
When making notes recently I felt like using a symbol for "a large amount of", and it occurred to me that surely others before me must have experienced the need for such a symbol.
What ...
user13571
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Why do I , J and K in mechanics represent X , Y and Z in maths?
Why are letters $i$, $j$, and $k$ used for axes names in mechanics while letters $x$ , $y$ and $z$ are used in mathematics?
Why these dimensions weren't called A, B and C or F, G and H?
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