Questions tagged [notation]

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

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48 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Who superseded Peano's dot notation in symbolic logic and when?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
88 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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55 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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Where did the bracket notation for vectors come from and is using parentheses to represent vectors valid?

In class I learned that a vector can be represented using <>, a column vector, and unit vector notation. However, one of the old math books that I study from notes that a vector in unit vector form ...
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1answer
114 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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2answers
136 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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73 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
56 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 more than ...
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461 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
159 views

Origin of existential quantifier symbol ∃?

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
242 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
81 views

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

In modern papers in statistics, it is common to use the sybmol $E[X]$ 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
119 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 ...
6
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1answer
249 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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770 views

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 ...
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246 views

Dimension of the candela unit: What does J stand for?

The J symbol can represent the unit of energy but it's also the symbol for the dimension of the candela (or luminous intensity). For the energy unit, it clearly comes from the family name of the ...
4
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1answer
131 views

Who changed $i$ to $j$ in electronics?

In electronics, $j$ is used for a square root of $-1$, because $I$ is current. Who introduced this and when? And was it really necessary, given that (at least now) current's symbol is capitalised? ...
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149 views

Is using ~ for “approximately equal” a relic of the typewriter and ASCII era?

In my life¹, I have never seen a symbol other than ≈ used in handwriting to express “approximately equal”. The symbol ~ was only used for more mathematical purposes such as equivalence, ...
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684 views

How did the obelus ÷ come to stand for division?

The obelus ÷ represents division on calculator keyboards, and sometimes in elementary education. It has a long non-mathematical history starting before 200 BC. Its ...
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1answer
117 views

The convention for speakers to refer to themselves at the board with a single initial

I found an interesting question on Math SE asked by @KCd, but it is over four years old without a clear answer. Since it seems to be more on topic here than on Math SE, I thought to post it here in ...
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315 views

How long has the order of priority of arithmetical operations been widely taught in high schools?

Browsing Facebook, I often come across posts like this, to test peoples' understanding of order of operations. This inevitably prompts a deluge of answers that either misunderstand the concept or ...
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92 views

Why does Michael Stifel's version of Pascal's Triangle look the way it does?

Today I've come across Michael Stifel's version of Pascal's Triangle, which I've seen referred to as the Figurate Triangle or the Triangle of Figurate Numbers as seen in Combinatorics: Ancient and ...
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88 views

Is it the 'd' or 'D' operator?

Philip J. Davis' article on the history of the gamma function (PDF) mentions how Leibniz proposed the iterated differential operator (p. 851 in the upper right corner, or p. 3 of the PDF, about half-...
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144 views

Communication using mathematical notation among people of different languages

Can it be (are there real examples/anecdotes of) that, say during international séminaires or conferences in mathematics, people of different linguistical origins could understand each other with the ...
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61 views

How did the proofs of uniqueness of additive inverses originate historically?

I have encountered various abstract algebra resources that prove the impossibility of number systems with plural additive inverses for a given element, generally through the substitution property of ...
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81 views

Who came up with a formula expressing the sign function in terms of the absolute value?

I read here and here that Karl Weierstrass used "| |" to indicate absolute value in 1841. The same sources indicate that Leopold Kronecker wrote of the sign function in 1878. Here it is indicated that ...
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Why are X and Y commonly used as mathematical placeholders?

I realize that X and Y are relatively popular terms when wanting to use a placeholder for an unknown English or math term. What is the origin of this term, and why was it X and Y; why not the other ...
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1answer
201 views

Origin of arcminutes, arcseconds, “arcthirds,” “arcfourths,” etc

This section of a Wikipedia article says [Modern time and angle notation] contrasts with the numbers used by Hellenistic and Renaissance astronomers, who used thirds, fourths, etc. for finer ...
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452 views

Notation for Christoffel symbols

In Christoffel's 1869 paper in which he introduced the Christoffel symbols on the 3rd and 4th pages, they are written as $\left[\substack{ij \\ k}\right]$ and $\{\substack{ij \\ k}\}$. The notation $...
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Earliest drawings of the plots of trigonometric functions

[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific ...
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1answer
427 views

When and why did $\frac{dy}{dx}$ become $\frac{d}{dx}y$?

It's obvious for us, that $\frac{dy}{dx}$ can also be written as $\frac{d}{dx}y$, but skimming through Leibniz or Eulers writings I couldn't see them write the latter. I speculate that this change ...
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598 views

Was English mathematics behind Europe by many years because of Newton's notation?

Below are several quotes suggesting that Newton's notation had the effect of retarding English mathematics by 50 years, 100 years, or even centuries. Here is my simplistic two-sentence historical ...
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161 views

What does the “G” for the similitude groups stand for?

When we have a bilinear symmetric/ bilinear anti-symmetric/hermitian form $b$ on a real/complex vector space $V$, one can consider the group of invertible matrices $A \in GL(V)$ which respect $b$, ...
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Notation $n=efr$ in algebraic number theory

When $\Bbb Q \subset K$ is a field extension of finite degree and when $p \in \Bbb Z$ is a prime number, the ideal $p O_K$ decomposes uniquely as a product $\prod_{i=1}^r P_i^{e_i}$ of prime ideals of ...
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168 views

Where does the letter S in “$S$-units” and in localization $S^{-1} R$ come from?

In number theory, we may encounter the notion of $S$-unit, $S$-integer, etc. where $S$ is a finite set of prime numbers (for simplicity). For instance, if $S = \{2,3\}$ then the $S$-integers are the ...
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What is the history and motivation for the (d-1,1) notation used to describe a field theory?

Very often in the literature of research papers and other articles, and maybe text books, on topics of quantum field theory, a theory may be described as a 3+1 or 0+1, or maybe even 1+1 theory. I ...
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1answer
192 views

D'Alembertian symbol $\Box$

The D'Alembertian is a generalization of the Laplacian operator to a space of arbitrary dimension and metric. Where does the D'Alembertian symbol $\Box$ come from? According to Wikipedia it has to ...
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1answer
120 views

Notation for fiber bundles - why E for total space?

I'm looking for info on why E is commonly used for the total space of a fiber bundle. I understand F (fiber) and B (base), but there doesn't seem to be any particularly obvious reason for choosing E.
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154 views

Who was the first to use the “does not exist” sign ∄?

Who was the first to use the "does not exist" sign ∄? I'm aware that Giuseppe Peano originated serifed ∃ and, moreover that Whitehead and Russell repurposed Peano's serifed ∃; I'm also aware that ...
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1answer
207 views

What is the origin of q-calculus notation?

It is kind of cute that q-analogues are used in physics (see this link for example), but it is also kind of confusing because the 'q' does not stand for 'quantum'. It predates that use! So, where ...
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221 views

Why is distance sometimes abbreviated S?

While distance in physical formulas is often abbreviated as d (which is pretty intuitive), another common abbreviation is s, as seen e.g. here, here or here. It also seems to be used in optics to ...
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141 views

First appearance of the product symbol ($\Pi$)

As far as I can tell, the first occurrence of the sum notation ($\Sigma$) was in Euler's book Institutiones calculi differentialis: Quemadmodum ad differentiam denotandam usi sumus signo $\Delta$, ...
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1k views

Why is kinetic energy denoted by the letter $T$ in quantum mechanics?

Kinetic energy is often written as $K$, $KE$ or $E_k$. Where does $T$ come from in quantum mechanics? Why and how did it come to be different?
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277 views

How were variables used and understood in (particularly) 19th century maths?

Context: I have been thinking about Frege's Begriffsschrift, where he introduces a version of what we now think of as the standard quantifier/variable notation. Philosophers who write on Frege tend to ...
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1answer
249 views

First appearance of tensor product symbol $\otimes$

I was asked recently if the tensor product symbol $\otimes$ had been used before Bourbaki's publication on multilinear algebra in 1948 (a draft of this document can be seen at http://sites.mathdoc.fr/...
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Notation for conditional probability

In mathematics terminology, a function is defined over two sets. One is is input set and other one is output set and for a particular input element, we the following notation $$f(x) = y$$ where $x$ ...
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124 views

Who was the first known mathematician to graph an equation?

A friend of mine pointed out that there were no graphs in Adam Smith's The Wealth of Nations, which was published in 1776. This surprised me because René Descartes (1596-1650) is well known as being ...
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449 views

Did Euler ever write $f(x)$, with parentheses?

Euler is often credited with introducing the notation $f(x)$, and people cite the example $f(\frac{x}{a}+c)$, where he had to use parentheses around the function argument. On the other hand, when the ...
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484 views

Instances of alternative notation being used for the trigonometric functions?

Consider the three "main" trigonometric functions, sine cosine and tangent; whose notations are sin(x); cos(x); tan(x). Are there instances of alternative notations being used for these particular ...
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722 views

Why is the Digamma function always denoted with the letter “psi”?

My question is on the notation of the Digamma function. The Factorial function $n!$ (which is met in secondary school), is conceptually seminal to the Digamma function. The Factorial function is ...