Questions tagged [notation]

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

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48 views

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

Where in Eulers writings could 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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44 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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1answer
446 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
141 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
233 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 ...
2
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1answer
80 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 ...
4
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1answer
117 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
207 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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543 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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2answers
153 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 ...
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1answer
128 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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138 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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589 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
115 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 ...
5
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2answers
291 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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88 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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2answers
143 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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60 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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3answers
3k views

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
174 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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415 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 ...
11
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1answer
303 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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548 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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143 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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159 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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48 views

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
181 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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114 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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146 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
191 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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1answer
209 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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137 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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994 views

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

I think the question is self-explanatory but stackexchange requires me to write something here.
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272 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
248 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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121 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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432 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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391 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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682 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 ...
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548 views

$\frac{dy}{dx}$ versus $\frac{{\mathrm d}y}{{\mathrm d}x}$

When I first learned calculus a few decades ago, the books I read used italicized letter "d"s in derivatives (like this: $\frac{dy}{dx}$). But a few years ago, I started seeing upright "d"s (like ...
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671 views

\mathbb versus \mathbf

When was the use of \mathbb popularized as an alternative to \mathbf? Of course there are the subjective preferences of certain authors, but when I read older articles, there appears to be an almost ...
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1answer
192 views

Origins of the Equals Signs

I asked this over on Math Stackexchange, and someone said it might be good to ask it over here too. Some authors use different equals signs for different purposes. For the most part, they are "$=$", "...
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294 views

How did Newton write his equations?

Once, after a lecture, my professor of differential equations said, that Newton did not use derivatives in his work as we do today. He told us that Newton rather used some series expansions for his ...
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317 views

Historical occurrences of mathematicians substituting terms for $x$ in the denominator of $\mathrm{d}y/\mathrm{d}x$?

This answer, to a question on teaching the chain rule, suggests writing something like this $$ \frac{\mathrm{d}\, \mathrm{e}^\sqrt{s}}{\mathrm{d}\,s}=\frac{\mathrm{d} \,\mathrm{e}^\sqrt{s}}{\mathrm{d}\...
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251 views

Examples of when the development of math notation accelerated progress in math research?

Sometimes, coming up with good mathematical notation is key to understanding parts of mathematics. For example, consider the quadratic formula. Brahmagupta formulated a version of the quadratic ...