Questions tagged [notation]

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

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193 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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144 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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132 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 ...
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208 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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1answer
101 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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71 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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204 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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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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1answer
307 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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1answer
176 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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185 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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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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1answer
153 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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1answer
408 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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109 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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92 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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1answer
96 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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1answer
73 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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130 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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2answers
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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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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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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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2answers
219 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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1answer
222 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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57 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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112 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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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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1answer
1k 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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1answer
127 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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107 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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168 views

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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1answer
159 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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133 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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1answer
140 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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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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1answer
114 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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181 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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1answer
128 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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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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1answer
626 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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216 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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1answer
92 views

Where did Euler prove 'his' theorem on homogeneous functions?

Where in Eulers writings can I find a proof of his homogeneous function theorem: $y$ is a homogeneous function of degree $k$ in $x_1,\ldots,x_n$ iff $ky = \sum_{i=1}^n x_i\frac{\partial y}{\partial ...
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1answer
315 views

What is the origin of "banana brackets"?

"Banana" brackets are used to denote catamorphisms: Another notation found in the literature is . These symbols are very similar to the composition of a $($ and a $|$, is this similarity ...
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513 views

Notation from Weyl's algebraic number theory book

In Weyl's "Algebraic Theory of Numbers", which was written in 1940, there are many symbols that look handwritten, such as Fraktur (or Sütterlin, whatever you want to call it) letters for ideals. His ...
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1answer
574 views

Why is the existential quantifier symbol ∃ a backwards "E"?

Peano introduced a number of logical symbols still used today: $∨$ (from Latin vel) $∧$ (inverted $∨$) $∃$ This inversion of Latin letters as symbols (and inversion of symbols to signify their '...
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1answer
313 views

Do North Koreans use Latin letters in their equations?

Do North Koreans use Latin (and Greek) letters in their equations? On the one hand, being such an isolationist country, I wouldn't be surprised if they used the Korean alphabet (조선글) in their ...
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1answer
127 views

Where does $M$ for expected value in Russian papers come from?

In modern papers in statistics, it is common to use the symbol $E[X]$ to refer to the expectation of a random variable $X$. While reading (a translated version of) "Convergence Rate of Nonparametric ...
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1answer
129 views

Were typographical variations between printings of the same journal article common?

In another question, I was asking about the origin of the reduced Planck's constant, $\hbar \equiv \frac{h}{2 \pi} .$ Specifically, I wanted to know why the symbol $`` \hbar "$ was selected for the ...
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1answer
514 views

Where did the term "set-builder notation" come from?

In math stack exchange I often see notations like $\{x\in\mathbb Q:x^2<2\}$ being called instances of set builder notation. When I went to school we (that is, I, my fellow students, my teachers, ...
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What is the origin of the $\hbar$ symbol?

Equations involving Planck's constant, $h ,$ are often simplified by instead writing them in terms of the reduced Planck's constant, $\hbar \equiv \frac{h}{2 \pi}.$ But where did the symbol for the ...