Use the convention tag for questions about standard, cultural practices in mathematics.

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1answer
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Scalar when undefined: real, complex, or something else

For an arbitrary vector space one defines, the scalar field can be anything: real, complex, rational, or some other previously defined field. However, in some texts on linear algebra for example, ...
0
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1answer
53 views

Why do we say pi is the ratio of the circumference to the diameter, and not diameter to the circumference?

Everywhere I see it written, $\pi$ is described as "the ratio of the circumference to the diameter". I know $\pi = C/d$, but the ratio $3.14...:1$ is $3.14$... diameters to $1$ circumference. So ...
0
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1answer
20 views

what are the formal names of operands of unary operations?

In case of binary operations, operands have formal names. Taking addition for example: $$a + b$$ We can formally call $a$ the augend and $b$ the addend. Names for operands are available in individual ...
0
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1answer
34 views

Vector in vector notation

I'm a bit confused as far as notationally differentiating between row and column vectors goes. Suppose I define a column vector $$\boldsymbol{a} = (a_{1}, a_{2})^{T}$$ and another column vector $$\...
3
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2answers
39 views

convention of a default atlas

Recently, I have been studying the basics of differential geometry and te necessary preliminaries. I arrived at the construction of differential structure on topological manifolds, where the non-...
0
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1answer
32 views

Do you think writing +-scalar is considered an acceptable convention?

I would like to know whether you think writing the following expression is considered acceptable: $$ 3x +-9 $$ Do writing $+-9$ as a way to express $+(-9)$ considered acceptable? I'm thinking about ...
3
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3answers
84 views

Is there a mathematical reason why rotation in the counterclockwise direction positive and clockwise rotation negative?

This inquiry has recently come to me in my study of trigonometry and the unit circle. It was said right from the very start that counterclockwise rotation were positive while clockwise rotations are ...
1
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1answer
54 views

Correct notation for presenting solutions to equations

Let's say I have a cubic equation $(x-a)(x+b)(x-c) = 0$, and I want to represent the solutions to this equation, what is the formal/conventional way that one would arrive and state the solution to the ...
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6answers
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No radical in the denominator — why? [duplicate]

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to $\sqrt{3}...
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3answers
2k views

The Degree of Zero Polynomial.

I wonder why the degree of the zero polynomial is $-\infty$ ? I heard that, it is $-\infty$ to make the formula $\deg(fg)=\deg(f)+\deg(g)$ hold when one of these polynomials is zero. However, if that ...
4
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2answers
26k views

Square root of a number squared is equal to the absolute value of that number [duplicate]

Possible Duplicate: Significance of $\displaystyle\sqrt[n]{a^n} $? The square root of a number squared is equal to the absolute value of that number. Why is $\sqrt{x^2} = |x|$? Why not just $x$...
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3answers
220 views

Product of permutation cycles, transpositions. Are there different conventions in the order?

From this answer I get that within each cycle you map each element to the one on the right, when taking the product of cycles the one on the right should be performed first, as a typical operator. ...
0
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2answers
33 views

How to express that one interval is included in another interval?

Would the symbol "$\in$" work for denoting that one interval is included in another interval? Like this: $(x>2) \in (x>0)$
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0answers
13 views

How do I show I've rounded to a certain decimal?

I noticed that we could say $\sqrt{0.9}\approx0.9$ if we round to one decimal, or $\approx0.95$ if we round to two decimals. But what is the correct way to show how many decimals we rounded to? ...
1
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0answers
20 views

Dimensionality of a function

When people refer to the "$x$-dimensional" case of a function or relation, how is the dimensionality determined? For example, let's say I have the functions $f(x,t)$ and $g(x, t)$. I could refer to ...
2
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0answers
51 views

Defining perpendicular lines in the 3D space

Is there a universal agreement about the definition of "perpendicularity" between two stright lines in the 3 dimensional euclidean space? Do they need to meet or it is enough to have perpendicular ...
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6answers
2k views

Why do we (mostly) restrict ourselves to Latin and Greek symbols?

99% of variables, constants, etc. that I run into are named for either a Latin character (like $x$) or a Greek character (e.g. $\pi$). Sometimes I twitch a little when I have to keep two separate ...
2
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1answer
36 views

Is there an agreed upon convention for naming ZFC+Large Cardinal Axioms?

Is there an agreed upon convention in general for what to name ZFC+[Large Cardinal Axiom]? Or would one have to state explicitly which axiom was being added? To explain what I mean, note that anyone ...
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0answers
22 views

Limit Terminology

From the $\epsilon-\delta$ definition of a limit, we can see that any limit can be broken up into two "one-sided limits". These "one-sided" limits are simple cases that arise as a consequence of the ...
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0answers
40 views

Product of Cycles: Name to denote “direction” of composition

Is there a notation to denote the difference between these two products of cycles? It seems as though there are two conventions out there that should have a specific name for them. The subscripts for ...
1
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2answers
22 views

Convention - Dual $\pm$ Signs

Say I have two equations like $$z+w=x+y$$ $$z-w=x-y$$ Is there any way I can combine these into a statement like $$z\pm w=x\pm y$$ I know the above statement is not correct as that entails 4 different ...
1
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1answer
18 views

Analogue of right-inverse for non-surjective function

Given a function $f: X \to Y$, not necessarily surjective, is there a common name (and more concise definition than follows) for a function which maps elements in $Y$ where $f$ is defined to elements ...
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2answers
28 views

Global decimal mark use

Is it feasible that one convention will be decided on with regard to the use of a decimal comma or decimal point and similarly, thousand separators? i.e. 1.000 vs 1,000
1
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1answer
19 views

A question about convention of writing identities and formulas

I'm only a third year undergraduate math student, but I've seen a decent amount of formulas, identities, and equations (at least enough to formulate such a question). However, I haven't actually ...
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2answers
24 views

Symbolic denotation of the space of all eigenvectors

There is a symbolic notation for the set of all eigenvalues $$\operatorname{spec} \varphi = \lbrace \lambda \in K \mid \lambda \textrm{ is an eigenvalue} \rbrace$$ There is also a notation for the ...
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0answers
18 views

Distribution functions: differentials in the numerator or denominator

One paper I'm looking at says, $n(M, z) \, dM \, dz$, the number of sources with mass $M$ at a redshift $z$, in the mass interval $dM$ occurring in the redshift interval $dz$. While another ...
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1answer
29 views

A Summation Convention – Substitution Rule

I'm new to this forum. I'm starting a PhD – it's going to be a big long journey through the jungle that is CFD. I would like to arm myself with some tools before entering. The machete is Cartesian ...
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1answer
79 views

Is there an open / established categorization / list of terms / concepts and synonyms for mathematics?

I am currently thinking about how to bundle some of the efforts of students to get / create good educational material. One idea of this little project (wiki-ed - still in the very early phase) is to ...
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2answers
51 views

How would this combinatorial process be written in conventional mathematical notation?

Now, I am going to define an operation on a list of numbers, which I will treat as a set, for want of a better approach. This may not be ideal, or even conventional, so apologies for lack of clarity ...
1
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1answer
61 views

Is there an analog of $\epsilon$ in complex analysis?

When someone writes let $\epsilon > 0$ in the context of calculus, we know the intention is that $\epsilon$ is real, and may be made as small as we like. Is there a corresponding symbol (Greek ...
4
votes
2answers
656 views

Convention of digit grouping after decimal point

I read that different cultures have different ways of grouping digits before the decimal point for readability e.g. 1234567890 can be grouped as 1 234 567 890 (English), 12 3456 7890 (Chinese) or 1 23 ...
12
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5answers
543 views

Why are the order-of-operations conventions good?

Children are sometimes taught silly mnemonics like "PEMDAS" to remember conventions on order of operations. (I never heard of "PEMDAS" until long after graduating from college, as far as I can recall....
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0answers
78 views

Handwriting cardinal numbers [closed]

In books the cardinal numbers are usually written with a gothic font. Is there any convention how to handwrite cardinal numbers, in particular, how to handwrite the continuum ($\mathfrak c$)
2
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0answers
46 views

When talking about periods of a function why is it common to introduce a factor of $2$?

In many books I have read, when talking about periodic functions, they tend to write the period as $2\omega$. Why do we need the $2$? I haven't come across any working where the factor of $2$ is ...
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0answers
50 views

asin, arcsin, $\sin^{-1}$ - is there any convention?

I've seen multiple forms how the arc sine is marked. But is there any convention which form is mostly being used? Does this depend on the country?
2
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1answer
43 views

Skeptical about (my understanding of) wikipedia's definition of a reflective subcategory.

I am self-learning category theory (though, at this point, I no longer remember what got me started), and I have encountered a troubling definition on wikipedia. The formal definitions of (full) ...
1
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1answer
28 views

What's the usual convention for directional derivatives in the $0$ direction?

Depending on the source, the definition of the directional derivative does not include the restriction that the direction vector be of unit length. In this case, it seems to me that we can then in ...
4
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0answers
68 views

Can a disconnected surface have a (negative) genus?

This question is rather about a convention. Is it possible (and conventional) to asign to, say the disconnected sum of two connected surfaces $X=\Sigma_h \sqcup \Sigma_g$ a genus? Since one has $\...
2
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1answer
25 views

Vocabulary question: singularity for an analytic map

I have a question that is purely on vocabulary. My native language is not english, so I would like to know the usual convention for the following. When people say "let $f: X \to Y$ be an analytic map"...
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5answers
827 views

$\{1,1\}=\{1\}$, origin of this convention

Is there any book that explicitly contain the convention that a representation of the set that contain repeated element is the same as the one without repeated elements? Like $\{1,1,2,3\} = \{1,2,3\}$...
6
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4answers
74 views

Is $\mp a$ actually different than $\pm a$?

So, the way I understand $\pm a$ as a general concept is basically as follows: $\pm a$ is really just two numbers, functions, or whatever $a$ represents, but the catch is that one of the $a$'s is ...
1
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1answer
113 views

What conventions surround the meaning of expressions like $\int \frac{1}{x} dx$?

I really struggle with the notation $\int f(x) dx$ because of the whole $+\,C$ thing, and this becomes double pronounced when $f(x)$ isn't defined everywhere. For example, we learned in high school ...
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5answers
2k views

use of $\sum $ for uncountable indexing set

I was wondering whether it makes sense to use the $\sum $ notation for uncountable indexing sets. For example it seems to me it would not make sense to say $$ \sum_{a \in A} a \quad \text{where A is ...
6
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3answers
119 views

Which is more simplified: $a\sqrt{b}$ or $\sqrt{c}$?

Which is considered more simplified (if it matters)? $a \sqrt{b}$ or $\sqrt{c}$ For example: $2 \sqrt{3}$ or $\sqrt{12}$
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0answers
33 views

“Second kind” orthogonal polynomials and functions

Recently I've been doing reading in the subject of orthogonal polynomials on the real line (OPRL). Such OPs arise in solving the three-term recurrence relation $$x u_n=a_{n+1}u_{n+1}+b_{n+1}p_n+a_{n}...
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1answer
166 views

What is $\varphi(0)$? [duplicate]

$\varphi$ is Euler's totient function. My question is: When/if $\varphi$ is defined at $0$, what is it usually defined as? Is there a "most natural" or more commonly accepted definition of $\varphi(...
0
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1answer
41 views

Conventions adopted for extended reals

It is known that $0^0$ despite being an indeterminate limit form, is usually defined to be equal to $1$. I wonder whether similar conventions exist for some other "indeterminate forms" in the context ...
4
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2answers
67 views

Conjugacy in $S_n$ with composing permutations left to right vs. right to left

I realize there are two conventions for composing permutations. Left to right: $(1\ 2)(1\ 3) = (1\ 2\ 3)$ Right to left: $(1\ 2)(1\ 3) = (1\ 3\ 2)$ Among others, Dummit and Foote and Contemporary ...
0
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1answer
121 views

Assignment of initial probability values

Suppose a coin is tossed until a head is observed for the first time. It is given that the coin lands heads with probability $p$ and tails with probability $1-p$. Based on only this information, can ...
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11answers
8k views

What is the average of no numbers?

I have two programs that both behave nearly identically: they both take in any numbers you give them and can tell you the average and how many numbers were given. However, when you don't give them any ...