# Tagged Questions

Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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### Confusion regarding terminology in Pressley's E.D.G

Here are two definitions taken from page $77$ of Pressley's Elementary Differential Geometry - $2$nd edition. Definition $4.2.1$ A surface patch $\sigma: U \to \Bbb R^3$ is called ...
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### Number of letters moved by a product of permutations

Let p and q be permutations in the symmetric group on n letters. p and q need not have the same cycle structure. Now compute q * inv(p) -- for inv(p) the inverse of p -- and count the number of ...
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### (Partial/total/well-) order vs ordering

Order or ordering – what is the difference? Is either correct? Is one British and one American English? Not exactly a maths question but probably still the best place to ask.
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### Terminology for a collection of paths

A path in graph theory is a "sequence of edges which connect a sequence of vertices" (from the Wiki page) Let $p_i$ denote a path between two vertices. Define $P = (p_1,\ldots,p_m)$ as a collection ...
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### A group specified by Generators and Relations.

I'm confused with some terms in several definitions. Is an alphabet of a free group the same thing as a generator set of any group? If it is right, then by a given alphabet (set of generators) can be ...
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### Can we use the terms 'class of sets' and 'family of sets' interchangeably?

I read in pg-4, Introduction to Topology and Modern Analysis by Simmons that class refers to a set of sets while family refers to a set of classes. I formulated an example for the same - if points are ...
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### When to use the plural form of “equation”?

For example, is the following a single equation or two equations? $$\frac{x-1}{2} = \frac{y-2}{-4} = \frac{z+3}{1}.$$ A textbook I'm looking at refers to the above as a single equation. But I would'...
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### Opposite terminology of relaxation

Removing a condition is a relaxation of a statement. What is the opposite? (i.e. adding a condition to a statement)
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### Show that in a binary tree, if B is the number of branch points (including the root) and L is the number of leaves, then one has the relation L = 1+B

We have been discussing trees lately, but have yet to even touch on the topic of a binary tree. I understand what a leaf is, but we didn't have one for the term "branch points" Without being 100% sure ...
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### What is the difference between closed-form expression and analytic expression?

What is the difference between closed-form expression and analytic expression? I often see them get referenced in settings where (in my opinion) they are essentially interchangeable. What is a ...
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### How to call a partition of $X$ which consists of all singleton subsets of $X$? [duplicate]

In other words, if $X$ is a set, then how do we call $Y=\{\{x\}:x\in X\}$? $\{X\}$ is already named the trivial partition, so that cannot be it. Complete partition and total partition did not yield ...
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### How are image and pre-image different from range and domain respectively?

How are image and pre-image different from range and domain respectively, in Layman's terms (as simple as possible)? Are they basically just keywords that often indicate more nuanced subsets of the ...
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### How to say increasing or decreasing as one word? Monotoneness?

In Calculus I, I can ask my class to "find the intervals of concavity". Is there a simpler way to say to say "find the intervals of increasing and decreasing"? In other words, "find interval of ...
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### What's uniform block signed permutations?

Let $[n]=\{1,2,\ldots,n\}$ and $P(n)$ the set of all partitions of [n]. A partition of $[n]$ is non-empty disjoint subsets of [n], called blocks, whose union is $[n]$. A block permutation of [n] is ...
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### Is there a symbol for always less than (or just always?)

For e.g, the quotient of $\frac{1}{n}$, $q$, where $n \gt 1$, $q$ will always be less than $1$. $$\frac qn\le n$$ etc. I can't really write $\frac {q}{n} < n$, because whilst true, it doesn't ...
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### What are higher dimension analogues of loops called?

A path $f:I\to X$ with the same starting and ending point $f(0)=f(1)=x_0\in X$ is called a loop. What is the higher dimensional analogue of a loop $f: I^n\to X$ called?
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### what is a ordinally quadratic function？

A function is ordinal equivalent to another means there exist a (unique) monotonic transformation between wiki definition of ordinal utility. I am a little confused, a function is ordinally quadratic ...
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