Questions tagged [notation]

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

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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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5 votes
1 answer
106 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&:=\...
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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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2 votes
0 answers
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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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3 votes
1 answer
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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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2 votes
0 answers
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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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1 vote
1 answer
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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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9 votes
0 answers
149 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 ...
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3 votes
1 answer
137 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 $B(2, 1)$....
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1 vote
0 answers
289 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 ...
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1 vote
0 answers
152 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?
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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 ...
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3 votes
3 answers
301 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 ...
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1 vote
1 answer
103 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 ...
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1 vote
0 answers
78 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 ...
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7 votes
2 answers
223 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 ...
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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 ...
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9 votes
1 answer
509 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 ...
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8 votes
1 answer
211 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&...
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  • 462
1 vote
2 answers
199 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 ...
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2 votes
0 answers
51 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: $$ ...
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2 votes
1 answer
172 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 $\sigma$ ...
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10 votes
1 answer
614 views

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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5 votes
3 answers
206 views

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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3 votes
0 answers
133 views

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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1 vote
1 answer
117 views

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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4 votes
1 answer
83 views

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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2 votes
0 answers
142 views

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 ...
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10 votes
2 answers
2k views

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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6 votes
0 answers
109 views

What is the origin in the discrepancy between engineers' and physicists' notation of waves?

my question is very simple. Physicists use this notation in order to write a (for example) plane wave: $$ \xi(z) = \xi^+ \mathrm{e}^{+\mathrm{i}kz} + \xi^- \mathrm{e}^{-\mathrm{i}kz}, $$ where $\xi^+$ ...
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3 votes
0 answers
142 views

Origin of notation "R with a stroke on the leg" for the square-root (℞)

The following text from Ars magna (1545) by Girolamo Cardano is known as the inception of complex numbers: "imaginaberis ℞ m 15" (You will imagine the square root of minus 15): The "R&...
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10 votes
2 answers
251 views

Who introduced the divisibility symbol $a\vert b$ ("$a$ divides $b$") and when?

I have just stumbled across this post and became curious about the same question, namely the part regarding the origin/history of the vertical bar symbol $a\vert b$ that we use to denote "a ...
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2 votes
1 answer
251 views

Differences between modern and old mathematical notations

Note: I didn't write the word "ancient" in the title because I want to see the notation from 1400 A.D. to 1700 A.D. Mathematical notation has changed very much from the past millennium, and ...
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1 vote
0 answers
72 views

First use of $K$ in notation for continued fractions

I will be giving a lecture soon (on Friday) about continued fractions. One of the historical compressed notations for continued fractions uses $K$ (from the German word for continued fraction): $$ ...
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5 votes
0 answers
125 views

How did Hertzsprung-Russell diagrams end up so confusing?

HR diagrams show in which of several sequences individual stars fall, each respecting the rough principle that hotter stars are of higher luminosity. (Sequences other than the main sequence may bend ...
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1 vote
0 answers
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Why did Sylvester Gates choose the name Adinkra?

Sylvester James Gates was one of the co-discoverers of Adrinkas. These are graphical representations of susy (supersymmetry) algebras. They are named after a West African people - the Akan of Ghana ...
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1 vote
1 answer
2k views

Where did the contour integral sign appear for the first time?

A simple question: Where did the contour integral sign appear for the first time? Wikipedia says that it was introduced by physicist Arnold Sommefield in 1917 ( Table of mathematical symbols by ...
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3 votes
1 answer
136 views

Why are the first three multiplicative SI prefixes lowercase?

The BIPM specifies twenty prefixes for the International System of Units (SI). All ten of the fractional prefixes are lowercase. However, only seven of the multiplicative prefixes are uppercase, the ...
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1 vote
0 answers
109 views

Origin of (f×g)(x) and (f∘g)(x) notations

Who and when began the writing of function multiplication, $f(x)×g(x)$, as $(f×g)(x)$ and of function composition, $f\big(g(x)\big)$, as $(f∘g)(x)$?
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3 votes
1 answer
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Why do we use $U$ for potential energy in classical mechanics?

I am unaware if someone has asked this before, but I am studying classical mechanics and I don’t know why do we use $U$ for potential energy. I have read that Rankine used it first, but I can’t find ...
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4 votes
1 answer
166 views

Has any large group of people used a base other than 10, 20 and 60 for ordinary purposes?

Wikipedia's list of numeral systems lists only $10,20,60$ as having been used in history. There are about twenty-five sets of symbols there used by different groups of people, but only three different ...
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5 votes
0 answers
171 views

Who introduced the comma notation for partial derivatives?

In general relativity, it is common to use the comma notation for partial derivatives $$\frac{\partial g_{\mu\nu}}{\partial x_\rho} = g_{\mu\nu_,\rho}$$ Where did this notation first appear? Was it ...
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0 votes
1 answer
154 views

History of points with coordinates notation

In this MathEducator StackExchange article, "Notation of points with coordinates", it's posed the question about what is the best notation for geometrical points and their coordinates: $P(3, ...
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2 votes
0 answers
45 views

First historical register of an improper fraction [duplicate]

I'm looking for the earliest known written register of an improper fraction, that is, a numerical fraction in which the numerator is greater than the denominator (like 3/2). By the way, who invented ...
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6 votes
1 answer
119 views

Origin of O/L for false/true in German computer-science texts

In Konrad Zuse's Plankalkül ZIA ID 0020 from 1972, in his patent submission Z23624 "Rechenmaschine" ZIA ID 0177 from 1936 and modern German Wikipedia article on the dyadic system, 2020-01-17 we see L ...
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4 votes
1 answer
224 views

Who superseded Peano's dot notation in symbolic logic and when?

Bertrand Russel gave an exhaustive treatment of creating mathematics from logic in Principia Mathematica (1910-1913), using the logical notation created by Frege and Peano. As monumental as this is, I ...
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1 vote
1 answer
140 views

History of exponential notation for the set of functions between two sets

It's well-known that if $A$ and $B$ are two sets, then the set of all functions from $A$ to $B$ can be denoted by $B^A$: explanations of this particular notation can be found in many places: https://...
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5 votes
0 answers
114 views

Why do Thai numerals look so different than Arabic numerals?

The Arabic numerals I am referring to are “1234567890”. I have read that Thai numerals, “๑๒๓๔๕๖๗๘๙๐”, are actually distantly related. Both descend from the numeral system invented by the Phoenicians, ...
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  • 151
7 votes
1 answer
1k views

Why do some people represent vectors with overbars while others use underlines?

When I was originally introduced to vectors, I was told to write them with an arrow above the variable, like so: $$\vec{x}$$ As soon as I began taking vector-heavy classes, I found that those ...
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  • 181
8 votes
2 answers
220 views

Origin of $\ll$ notation

Vinogradov introduced the notation $$f(x) \ll g(x)$$ to denote that for some $C>0$, we have $|f(x)|\leqslant C\,g(x)$ for all $x$ under consideration; usually for all $x$ larger than a fixed ...
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