Questions tagged [notation]

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

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113 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
125 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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118 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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254 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
105 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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254 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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82 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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81 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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133 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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59 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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79 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
141 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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308 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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91 views

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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198 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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457 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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103 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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69 views

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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146 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
160 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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100 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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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
154 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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185 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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131 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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676 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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267 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
219 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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115 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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400 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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266 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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571 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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472 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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536 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
155 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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251 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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238 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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241 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 ...
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Why were the SI-unit prefixes chosen to be a multiple power of 3?

Why were the SI unit prefixes, i.e. \begin{align} \mathrm{giga} && 10^9 \\ \mathrm{mega} && 10^6 \\ \mathrm{kilo} && 10^3 \\ \mathrm{milli} && 10^{-3} \\ \...
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193 views

What is the name of this numeral system?

In a XVth century french manuscript on arithmetic and astrology, there is a description of a numeral system as follows (it starts here in the manuscript). Numbers between 1 and 9 are depicted by a ...
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186 views

What are early examples of the rare notational convention to make the sign of the real number represented by a letter depend on the typography?

Question. What early published or citably attested examples (preferably in the mathematical literature) can you give of the following convention? Let $\mathbb{S}$ denote some nonempty subset of some ...
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671 views

Why is the letter $\vec{r}$ used for position?

I'm sorry if this is a dumb question but I've never heard a convincing explanation for why seemingly all of physics names the position vector "$\vec{r}$". I've tried translating it into just about ...
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69 views

Has the modern logic negation $\lnot$ been adapted from Frege's Begriffsschrift?

Has the modern logic negation $\lnot$ been adapted from Frege's Begriffsschrift?
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468 views

Is the prime notation for derivatives $f'$ due to Euler?

Cajori, the website on Earliest Uses of Symbols of Calculus and many other sources claim that Lagrange introduced the notation $f'(x)$ for the derivative of $f(x)$ with respect to $x$. But I see Euler ...
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229 views

Notational change with Integrals

A little over 50 years ago I took my first Calculus class and learned the conventional form of an integral as: $$ \int f(x)\,\, \textrm{d}x $$ That is, the integral sign (definite or indefinite) ...
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421 views

Why do we write $E=mc^2$ and not $E=c^2 m$?

My question goes from Phys.SE where people advised me to ask my question here. I always learn in maths and physics when something is a constant in an equation we have to put it before which varies. ...
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1answer
3k views

Old square bracket notation for units

As discussed in this answer https://physics.stackexchange.com/a/77691/667 there are several common conventions for the notation $[q]$ of a physical quantity $q$. However, I often see people to put ...