Questions tagged [notation]

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

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1answer
285 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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2answers
152 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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2answers
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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1answer
286 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 ...
4
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1answer
264 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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1answer
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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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0answers
130 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 ...
5
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2answers
472 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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1answer
581 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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2answers
893 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 ...
10
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3answers
647 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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0answers
984 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
258 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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1answer
373 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 ...
8
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1answer
343 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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4answers
279 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 ...
2
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2answers
5k views

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} \\ \...
7
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1answer
234 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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1answer
194 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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4answers
1k 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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1answer
77 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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2answers
622 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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247 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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1answer
552 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
6k 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 ...
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2answers
147 views

Why $x_a$ (or $x_o$) and not $a_x$? (conventions for algebraic quantities)

It's my understanding that the convention of using letters from the end of the alphabet ($x$, $y$, $z$) to represent $variables$, and letters from the start of the alphabet ($a$, $b$, $c$) to ...
4
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1answer
276 views

Why is the action from the principle of least action traditionally denoted $S$?

In theoretical physics, a Hamiltonian is traditionally denoted by some variant of $H$, a Lagrangian is some variant of $L$, but why is an action always some variant of S (as opposed to, say, $A$)? ...
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2answers
540 views

Is the symbol for set membership $\in$ derived from greek letter $\epsilon$?

Title self explains: Is the symbol for set membership $\in$ derived from greek letter $\epsilon$? What is their historical relationship? Obviously the letter must be older, since greek alphabet is ...
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1k views

When was the function arrow notation $x \mapsto y$ first used?

The notation $x\mapsto \sin x $ and its meaning are well-known to most mathematicians. Less well-known seems to be the fact that $x \mapsto y$ means the same as Church's $\lambda x.y$ and Frege's $\...
3
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1answer
263 views

First use of litte $o_p$ (little $o$ in probability) notation?

I have a follow up question from my previous question on math.SE, where I asked about the First use of little $o$ notation - for those who want to check - the answer goes back to Landau ($1909$), this ...
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1answer
530 views

Who invented the divisibility symbol and why is it backwards?

When we want to perform division, we write e.g. $8/2$ (this is what we already learn at school). But when we want to express that $2$ is a divisor of $8$, we write: $2\mid 8$. What the heck?? I do ...
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1answer
723 views

Why did I learn to write the base of the logarithm differently from the rest of the world?

It only occurred to me recently, in connection with this MO posting, that the way I write the base of the logarithm is not shared by the rest of the world. I am Dutch, and I learned at school to write ...
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1answer
92 views

reference need about History of prime number development

Im trying to connect my study to a breif history of prime numbers . Also im interesting in reading history of numbers how they come and how they developed . So can any one suggest for this question a ...
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1answer
398 views

What is the history of using $i$/$\iota$ as the imaginary unit?

I'm interested in particular in knowing about when $\iota$ began to be used as the imaginary unit/who began to use it. A majority of all text books that I have seen tend to just use $i$ as the ...
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2answers
389 views

Who introduced the notation $y|_{x=a}$?

When a variable $y$ depends on other variables, say $y=c x^3$, one often writes $$y|_{x=2}$$ to say "$y$ when $x$ has value $2$". This might be more familiar in the context of derivatives where we ...
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2answers
1k views

Why is the thermoelectric figure of merit denoted by $ZT$?

Why is the thermoelectric figure of merit denoted by $Z T$? Does $Z T$ come from the abbreviation of words in some language? Update: So far, $T$ has been figured out — it is the temperature, to make ...
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1answer
238 views

Why do we use brackets for function parameters?

I know that a function is called "function" because it's an "execution" of operations. Abbreviated notation is f. But why do we write f(x) and not ...
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27k views

Who first defined the “equal-delta” or “delta over equal” ($\triangleq$) symbol?

The symbol $\triangleq$ is sometimes used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C). The notation $t \triangleq ...
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2answers
309 views

Introduction of $\imath$ and $\jmath$ notations for the imaginary unit

The imaginary unit is generally denoted $i$ or $\imath$. I have learned that the term imaginary ("imaginaires") was coined by R. Descartes in 1637, and the "i" notation was introduced by L. Euler (cf. ...
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423 views

Is the symbol $e$ for the base of natural logarithm honoring Euler?

According to Internet (actually, Wikipedia and Wolfram MathWorld), I have two information: It was Euler who first introduced the symbol $e$ (before people used $b$); the symbol is to honor Euler. ...
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2answers
925 views

Where did John Wallis get the idea for $\infty$?

I read in an offhand comment in Amir Alexander's 2014 book Infinitesimal (p.280), that John Wallis introduced the symbol $\infty$ for infinity. Was there any logic, reason, or precedent for this ...
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1answer
143 views

What is rationale or history for using the symbol $\partial{U}$ to represent surface boundary?

There are many examples where the notation of $\partial{U}$ is used to represent the surface boundary of some volume $U$. For example, the following representation of the Divergence Theorem: $$ \...
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1answer
396 views

Abbreviated Notation for Groups, Rings and Fields

Groups, Rings and Fields are often referred to by the set involved without mention of the operation(s). For example, the "group (G,+)" may be called the "group G". When did this practice originate ...
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2k views

Who gets credit for the real numbers?

If Simon Stevin already pioneered the unending decimal representation for every number (rational, surd, etc.) at the end of the 16th century, why do Cantor and Dedekind (who certainly gave a more ...
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82 views

Whence originates the use of the nabla (∇) for a connection or covariant derivative?

Who introduced it, when, where, and with what if any rationale? (Note that I am not asking about the origin of the nabla symbol, which is covered here.)
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1answer
934 views

How did the bra-ket notation become mainstream in quantum mechanics?

I noticed that Dirac bra-kets and their algebra are very much like the linear algebra. A ket is like a vector, a bra is like the conjugate transpose of a vector, a bra-ket is like a complex inner ...
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1answer
272 views

How did the exterior product get its symbol?

As per the title: where did the notation $a\wedge b$ for the exterior product of $a$ and $b$ originate, and/or who popularised it? I'm especially interested in motivation for the choice of this symbol ...
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180 views

Why is the space of sections of $E$ called $\Gamma(E)$?

The space of sections of a bundle $\pi: E \to B$ is commonly denoted $\Gamma(E)$. (Note that the graph of a function $f$ is $\Gamma(f):=\left\{(x,f(x))\right\}$, and a particular section $\sigma: B \...
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1answer
799 views

First use of curly braces to denote a set?

I was wondering who was the first person to Use curly braces to represent a finite set. Exempli gratia, $\{1,2,3\}$. Use set builder notation. Such as $\{2n:n \in \mathbb{Z}\}$ to represent the even ...
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5answers
753 views

Who invented the Leibnitz notation $\frac{d^2y}{dx^2}$ for the *second* derivative?

This MSE question made me wonder where the Leibnitz notation $\frac{d^2y}{dx^2}$ for the second derivative comes from. It does not arise immediately as the obvious generalization of $\frac{dy}{dx}$. ...