# Questions tagged [convention]

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

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### Ring theory conventions - Zero ring, local homomorphisms

Just wondering about conventions dealing with the zero ring and the zero scheme. Does the category of schemes have an inital object? Is the zero ring considered local? For the purposes of scheme ...
17 views

### Is there a best practice for naming mathematical objects? [closed]

Does anyone know of a guide for selecting (single letter) names for variables and functions etc. in an applied mathematics text when there is no established standard?
48 views

### Why $T_pM$ instead of $TM_p$?

If $E\to M$ is a fiber bundle, it's convention to write 1. $E_p$ for the fiber at $p$, 2. $E^*$ for its dual bundle. Exceptionally, for the tangent bundle $TM\to M$ almost every author writes 1. $T_pM$...
43 views

### What are the domain and values of binomial coefficients $n \choose k$ for any integer $n$ and $k$, and why?

This is a question about "nasty details" of the binomial coefficients. I would like to understand the definition of binomial coefficients $n \choose k$ for general integers $n$ and $k$. ...
36 views

### Dot product with Einstein summation convention (index notation)

My professor, when proving: $$a \cdot b = a_ib_i$$ wrote: $$(a_i \hat{e}_i)\cdot(b_j \hat{e}_j) = (a_ib_j)(\hat{e}_i\hat{e}_j)$$ My doubt is: Are we allowed to treat the dot product as ordinary ...
92 views

### Why use random variables instead of probability spaces

When talking about various ways to model something probabilistically, many authors prefer to use random variables, instead of probability distributions. Of course, this difference is more of a point ...
65 views

### In standard set theory is a statement containing both a union and intersection but no parentheses disallowed?

Most discussions of set theory with which I am familiar assign equal operator precedence to $\cap$ and $\cup$. This may sound like a ridiculous question, but I never thought about, nor do I recall ...
124 views

### confusion regarding treatment of $dx$ in a physics problem

Consider a fixed, positive Point charge $q1$, kept at the origin. Another (positive) charge, $q2$, is being brought from $\infty$ to the point $(r,0)$, by an external agent slowly. We wish to ...
60 views

### Can an axiom in FOL have recursion?

Lately, I've been interested in playing around with seeing how powerful a set theory can be with a single axiom. A while, ago I made this naive axiom schema; dubbed the axiom schema of propagation (...