1
vote
1answer
75 views

Why $1\frac{1}{2}\ne \frac{1}{2}$?

Why mathematicians have chosen notation such that in algebra $1\frac{1}{2}=\frac{3}{2}$ but $x\frac{y}{z}=\frac{xy}{z}$, instead of $x\frac{y}{z}=\frac{xz+y}{z}$?
7
votes
2answers
97 views

Why does the sign $\times$ vanish in mathematical expressions?

I just would like to know whether or not there exists an historical reason to prefer the expression $a b$ to $a \times b$. Why does the sign $\times$ vanish (whereas $+$ stays)? I thought that ...
4
votes
2answers
120 views

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?
21
votes
3answers
675 views

Who named “Quotient groups”?

Who decided to call quotient groups quotient groups, and why did they choose that name? A lot of identities such as $$\frac{G/A}{B/A}\cong \frac{G}{B}$$ suggest that whoever invented the notation ...
3
votes
2answers
130 views

What is the intutive explanation of why the notation of matrices is as it is?

If I want to solve a system of linear equations, like 2x-y=1 x+2y=4 Then the matrix notation for the same would be: $$ \begin{bmatrix} 2 & -1 \\ 1 & 2 \\ \end{bmatrix} \begin{bmatrix} X\\ ...
3
votes
1answer
92 views

Coincidence about nabla?

I was surprised to notice that gradient of function and Levi-Civita connection have the same notation, i.e. nabla sign $\nabla$. Moreover, extending any connection on tensors, one let it be ...
1
vote
1answer
98 views

is the decimal notation the “right” notation for arithmetic?

I am considering here the pre-decimal notations such as Roman numerals, Egyptian numerals etc. It seems reasonable that these must all be equivalent. And it seems that decimal notation (i.e. ...
13
votes
0answers
116 views

How and why did Weierstrass $\wp$ get its special symbol?

I kind of always hated drawing the Weierstrass $\wp$ symbol by hand, and it struck me as odd how and why it achieved its special status in the first place. After all, there are tons of other important ...
2
votes
1answer
64 views

History of the Coefficients of Elliptic Curves — Why $a_6$? [duplicate]

I would like to know what is the motivation behind the naming convention of the Weierstrass form of elliptic curves given as $$E:y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6.$$ I can see that $a_1,a_2,a_3,a_4$ ...
11
votes
3answers
707 views

History of notation: “!”

Does anyone know where the factorial "!" symbol came from? I can't decide if it is my favorite or least favorite notation in mathematics...
2
votes
1answer
80 views

The meaning of Differentials in Integration

This is further to the questions discussed in a previous post Here is an example of what I mean: Suppose that $C$ is a closed path in the plane and consider the line integral of $xy\,dx+x^2\,dy$ over ...
5
votes
1answer
82 views

Who introduced the finite difference notation using $\Delta$?

We all know that Leibniz introduced the differential notation $dx, dy$, and that in developing his calculus for infinitesimal differences he was inspired by his previous work on finite diffences. ...
15
votes
10answers
1k views

Challenge: Demonstrate a Contradiction in Leibniz' differential notation

I want to know if the Leibniz differential notation actually leads to contradictions - I am starting to think it does not. And just to eliminate the most commonly showcased 'difficulty': For the ...
7
votes
1answer
109 views

First usage of the symbol ∈

Concerning a book [1] I am reading the symbol $\in$ was first used by Giuseppe Peano and is the first letter $\epsilon$ (epsilon) of the word ἐστί (means "is"). Does anyone know in which work of Peano ...
2
votes
3answers
64 views

Why the name “umbilic”?

Umbilic points are points on a surface at which the principle curvatures of the surface are equal. "Umbilic(al)" refers to the navel/belly button. But why do we call these points so? What about the ...
3
votes
2answers
240 views

How is it that treating Leibniz notation as a fraction is fundamentally incorrect but at the same time useful?

I have long struggled with the idea of Leibniz notation and the way it is used, especially in integration. These threads discuss why treating Leibniz notation as a fraction and cancelling ...
3
votes
0answers
113 views

Why do Mathematicians use $u$ and $v$ as variables?

I'm sure this has happened to you as well: you are reading some hand-written work, the variables used are $u$ and $v$, and at some point the handwriting becomes unclear and you cannot distinguish the ...
11
votes
1answer
168 views

Why is $e$ the Identity?

Some authors use $e$ to be the identity element of a group instead of $1$. What is the origin of this notation? Was this before or after we used $e$ to represent the base of the natural logarithm? ...
11
votes
4answers
174 views

The origin of the function $f(x)$ notation

What are the historical origins of the $f(x)$ notation used for functions? That is when did people start to use this notation instead of just thinking in terms of two different variables one being ...
10
votes
5answers
522 views

What are reasons why some symbols in mathematical logic are not standardized?

Why is so hard to find a standardisation regarding symbolism and/or terminology in Mathematical Logic ? We see again and again students asking if e.g. $\rightarrow$ and $\implies$ means the same ...
3
votes
2answers
105 views

Notation and the name choice for meet and join (in order theory)

I have two simple questions: From where do the names meet and join come from? I don't see any intuition between those names in context of order theory. From where does the notation come? I have to ...
1
vote
1answer
77 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
2
votes
1answer
159 views

Why do we write $f : X \rightarrow Y$ as opposed to $f \in X \rightarrow Y$.

I've always been taught to write $f : X \rightarrow Y$ as opposed to $f \in X \rightarrow Y$. This seems weird though, since $X \rightarrow Y$ can be viewed as the set of all functions with source $X$ ...
3
votes
2answers
156 views

Notation: Why do we learn to write the higher powers in an equation first?

I have always written equations in the form $y=ax^2+bx+c$ but after entering an equation into Wolfram Alpha I noticed that the answer was displayed in the form $y=c+bx+ax^2$. I know that there is no ...
76
votes
24answers
6k views

What are some examples of notation that really improved mathematics?

I've always felt that the concise, suggestive nature of the written language of mathematics is one of the reasons it can be so powerful. Off the top of my head I can think of a few notational ...
0
votes
0answers
43 views

Alternate convention in matrix multiplication?

I'm going through Halmos's Finite-Dimensional Vectorspaces. I noticed an oddity in a proof where the indexes seemed to be swapped when multiplying a matrix by a vector. I went back about 30 pages to ...
7
votes
4answers
230 views

Is there an established notation, either modern or historical, for any unit of measure which is then further subdivided into 360 degrees or parts?

This question about notation is simple as dirt, but would be useful for me regardless, because of some work that I'm doing in music theory. Basically, while there's a notation for subdividing the ...
6
votes
0answers
133 views

Origin of $\mapsto$ notation

Who invented the brilliant $\mapsto$ notation for describing a function's action on a point, as in $x \mapsto x^2$? This is in some sense a counterpart to Who came up with the arrow notation $x ...
7
votes
1answer
177 views

On the pronunciation of the second derivative

I have been looking at Lancelot Hogben's Mathematics for the Million (first published in 1936). In the chapter on calculus he says that the second derivative $\displaystyle \frac{d^2y}{dx^2}$ is ...
3
votes
1answer
87 views

Numerator and denominator separated by hyphen

This is a question about historical notation practices. A colleague recently sent me a scan of a portion of a 1935 paper: P. R. Bassett. "Passenger Comfort in Air Transportation", Journal of the ...
8
votes
2answers
480 views

Notation for intervals

I have frequently encountered both $\langle a,b \rangle$ and $[a,b]$ as notation for closed intervals. I have mostly encountered $(a,b)$ for open intervals, but I have also seen $]a,b[$. I recall ...
1
vote
1answer
89 views

backwards membership notation set theory

This is more of a notational/historical question. I had a course last quarter where the professor would write things like $A \in x$ for $A$ a subset of some bigger space $X$ and $x$ an element of $X$. ...
4
votes
1answer
68 views

Is the Knuth arrowup notation defined for non-natural exponents?

I recently found out about Knuth's arrowup notation. Wikipedia, among other websites, only shows a definition for $a \uparrow^n b$ where $n \in \Bbb{N}_0, a \in \Bbb{R}, b \in \Bbb{N}$ as following: ...
3
votes
3answers
353 views

What do these old symbols from set theory mean? (Large E, $\cdot$ and $+$ for sets, and $\ \bar{\!\bar X}\,non\!\geqslant\frak n$)

So, I'm trying to prove the theorems in this paper by Tarski: On Well-ordered Subsets of any Set, Fundamenta Mathematicae, vol.32 (1939), pp.176-183 but it is from 1939, and I don't recognize a few ...
2
votes
2answers
68 views

Why is $S/R$ a ring extension?

If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
9
votes
1answer
737 views

What is the name of the $\in$ symbol and where does it come from?

It looks like a lower-case epsilon, but the Wikipedia page on epsilon states that they are not the same. Does this symbol have a typographic identification outside of mathematics? Where did the ...
0
votes
0answers
19 views

Notation used for H in Hyperbolid geomtry metric

This is suppose to be understood as $H_2^2$ Taken from the full equation : from lecture 3 of Cosmology on youtube by Leonard Suskind Can anyone please give some information on the notation ( ...
4
votes
0answers
41 views

Symbol for function composition [duplicate]

Possible Duplicate: History of $f \circ g$ Choice of symbols can be an indicator of intellectual allegiance. Consider how, back in the day (and before LaTeX regularised things so much!), ...
4
votes
3answers
526 views

Where did these symbols come from?

Where did these symbols come from? Like Pi, Fee and this weird E/sideways M and the triangle.
10
votes
2answers
413 views

What do Greek Mathematicians use when they use our equivalent Greek letters in formulas and equations?

Like for example, it's common to use the Greek letter $\theta$ to represent an angle right? So what would a Greek person doing math use to represent an angle? Would they also use $\theta$? Or is there ...
0
votes
1answer
80 views

Two $\psi$ functions

This is either a notation/history question or a point of confusion. In (for example) Ramanujan's proof of Bertrand's postulate, he uses the following notation: $\log [x]!$ means $\log ([x]!),$ in ...
5
votes
1answer
208 views

History of Lie algebra notation (in Fraktur)?

Does anyone know how it has become the standard to express Lie algebras in fraktur? I'd also like to know how it's established for each era and region, not only the origin. It doesn't seem that ...
10
votes
2answers
215 views

Articles on ideas in the history of mathematics notation?

I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
2
votes
3answers
233 views

Is there a reasoning behind the depiction of the numbers as they are $\{1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9\}$?

Is there a reasoning behind the depiction of the numbers as they are: $$\{1,2,3,4,5,6,7,8,9\}$$ Is there any other form of depiction for $6$ and $9$ other than $VI$ and $IX$?
10
votes
2answers
1k views

Which symbol should be used for an empty set?

Currently, a discussion started on the German Wikipedia article for Empty Set (the German discussion), whether $\emptyset$ or $\varnothing$ should be used or is more common as a symbol for an empty ...
61
votes
5answers
2k views

Why does mathematical convention deal so ineptly with multisets?

Many statements of mathematics are phrased most naturally in terms of multisets. For example: Every positive integer can be uniquely expressed as the product of a multiset of primes. But this ...
5
votes
1answer
553 views

Who came up with the arrow notation $x \rightarrow y$?

I read that the arrow notation $x \rightarrow y$ was invented in the 20th century. Who introduced it? Each map needs both an explicit domain and an explicit codomain (not just a domain, as in ...
4
votes
2answers
211 views

Analytic versus Analytical Sets

Browsing MathOverflow I came across a question about analytical sets. Through the discussion following a comment made by our very own Asaf, I learned that bold face $\mathbf{\Sigma^1_1}$ and light ...
7
votes
0answers
489 views

How do Greek mathematicians name variables? [closed]

I've always wondered how people in Greek name variables that other people use greek letters e.g. $\theta$. They use latin?
6
votes
4answers
1k views

History of $f \circ g$

$f \circ g$ is usually interpreted as $f(g(x))$ although, as Google shows, $g(f(x))$ is used frequently too. My question: Does anybody know who was the first mathematician to use this symbol and what ...