# Tagged Questions

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

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### 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 ...
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### 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 ...
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### 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-...
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### 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 ...
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### 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 ...
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### 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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### 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. ...
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### 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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### 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? ...
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### 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 ...
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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### 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
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### 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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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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 ($\mathfrak c$)
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### 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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### 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?
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### 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) ...
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### 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 ...
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### Writing a Series of Equalities and Inequalities across Several Lines

What is the convention for writing a series of successive equalities and inequalities across multiple lines? Let me explain. Let $E_k$ denote an expression; for example, $E_0$ could be a sum or an ...
In this paper http://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf at the end of chapeter 2 the author says that in index notation a matrix is written as $A^\mu_{\;\;\nu}$ and its ...