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Questions tagged [notation]

For questions about the history and development of how symbols and related objects are written.

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Notation for Propositional values in Church's "Simple Theory of Types"

In Alanzo Church's "A Formulation of the Simple Theory of Types" (The Journal of Symbolic Logic 5 no.2 (1940) 56--68, DOI:10.2307/2266170), he adopts the ...
Alex Nelson's user avatar
1 vote
1 answer
104 views

David Hilbert's paper: Substitution of the group of cyclotomic field

A question about a notation in David Hilberts's "Ein neuer Beweis des Kroneckerschen Fundamentalsatzes über Abelsche Zahlkörper" (here a german online available source, not sure if there ...
user267839's user avatar
0 votes
0 answers
54 views

Why is the standard deviation bias correction factor called c₄?

The term to remove bias from an estimate of standard deviation for a normal distribution is referred to as $c_4$. What is the origin or reason for using that notation for the correction factor?
feetwet's user avatar
  • 101
3 votes
2 answers
192 views

Seeking Comprehensive References on the History of Scientific Notation

I am on a quest to uncover the rich tapestry of history surrounding scientific notation as a way of expressing numbers. Specifically, I'm interested in scholarly books, peer-reviewed articles, and ...
Humberto José Bortolossi's user avatar
13 votes
1 answer
1k views

What was the motivation for the choice of the subset symbol?

I gather that the symbols $\subset$ and $\supset$ were introduced by Ernst Schröder in his 1890 Vorlesungen über die Algebra der Logik. This account also appears—attributed to good old Cajori—in an ...
Paul Tanenbaum's user avatar
3 votes
0 answers
158 views

How did Hindu-Arabic Numerals get their shapes?

I’ve noticed a recurring post on social media that presents an image suggesting the shapes of Hindu-Arabic numerals are connected to the angles within their design: This claim seems dubious to me. I ...
Humberto José Bortolossi's user avatar
1 vote
0 answers
108 views

Historical Accounts of Confusion in Alphabetic Number Systems?

I’m delving into the intriguing world of alphabetic number systems (greek, for instance), where letters serve a dual purpose—forming words and representing numerical values. I’m curious about the ...
Humberto José Bortolossi's user avatar
4 votes
1 answer
126 views

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 $\...
Timothy Chow's user avatar
  • 1,516
-3 votes
1 answer
147 views

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&...
Humberto José Bortolossi's user avatar
2 votes
1 answer
643 views

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 ...
Rivers McForge's user avatar
2 votes
0 answers
76 views

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 ...
Elías Guisado Villalgordo's user avatar
1 vote
0 answers
42 views

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 ...
scarface's user avatar
  • 183
3 votes
1 answer
112 views

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-...
Charles's user avatar
  • 131
3 votes
0 answers
97 views

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 ...
Francisco José Letterio's user avatar
1 vote
0 answers
86 views

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.
David Moldes's user avatar
29 votes
2 answers
1k views

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 ...
MIKANkankitsu's user avatar
3 votes
0 answers
274 views

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 ...
Scott H.'s user avatar
  • 131
1 vote
0 answers
57 views

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. ...
ististyle's user avatar
  • 303
2 votes
2 answers
637 views

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 ...
Humberto José Bortolossi's user avatar
1 vote
0 answers
113 views

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 ...
edpidufd's user avatar
1 vote
0 answers
104 views

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. ...
Thomas Anton's user avatar
1 vote
1 answer
405 views

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.
Humberto José Bortolossi's user avatar
2 votes
0 answers
124 views

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 ...
Frode Alfson Bjørdal's user avatar
5 votes
1 answer
112 views

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 ...
Sam Gallagher's user avatar
10 votes
1 answer
207 views

History of greater-than symbol used in reverse?

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 ...
Joseph O'Rourke's user avatar
14 votes
2 answers
2k views

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 ...
Shaikh Ammar's user avatar
4 votes
1 answer
538 views

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 ...
Rohit Joshi's user avatar
2 votes
1 answer
130 views

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)...
spicy_potatoes's user avatar
15 votes
1 answer
409 views

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 ...
Torsten Schoeneberg's user avatar
6 votes
1 answer
162 views

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&:=\...
Slate's user avatar
  • 163
1 vote
1 answer
76 views

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 ...
Galen's user avatar
  • 309
2 votes
0 answers
143 views

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 ...
Mitch's user avatar
  • 191
4 votes
2 answers
1k views

Why is electric potential denoted by $\phi$?

I haven't found any explanation for it, and I'm curious.
EB97's user avatar
  • 149
3 votes
0 answers
107 views

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 $K$?
D.R's user avatar
  • 253
1 vote
1 answer
79 views

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..." -...
Tom Barson's user avatar
11 votes
0 answers
278 views

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 ...
Jukka Kohonen's user avatar
3 votes
0 answers
183 views

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 $B(2, 1)$....
user477398's user avatar
1 vote
0 answers
919 views

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 ...
electrical apprentice's user avatar
1 vote
0 answers
253 views

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?
Schilive's user avatar
  • 111
1 vote
0 answers
145 views

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 ...
user avatar
6 votes
3 answers
2k views

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 ...
BigbearZzz's user avatar
1 vote
1 answer
105 views

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 ...
bblohowiak's user avatar
1 vote
0 answers
118 views

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 ...
Greg Nisbet's user avatar
7 votes
2 answers
319 views

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 ...
user avatar
25 votes
6 answers
2k views

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 ...
user avatar
11 votes
1 answer
2k views

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 ...
Rax Adaam's user avatar
  • 484
8 votes
1 answer
350 views

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&...
Rax Adaam's user avatar
  • 484
1 vote
2 answers
293 views

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 ...
yolo's user avatar
  • 113
3 votes
0 answers
57 views

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: $$ ...
Rob Arthan's user avatar
2 votes
1 answer
349 views

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 $\sigma$ ...
KCd's user avatar
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