0
votes
2answers
37 views

Beginner questions about Sets.

I have a quick question in regard to sets. I am a little confused when I see the notation $A\subseteq B$. How is this different than the sets $A$ and $B$ being identical? I guess some of the confusion ...
3
votes
2answers
63 views

Should “together with” be taken as slang for an n-tuple?

When an algebraic structure is defined, it is often defined as a set $S$ "along with"/"together with"/"having" operations $\circ_1, \circ_2, \ldots, \circ_n$, and "denoted" by $(S, \circ_1, \circ_2, ...
0
votes
1answer
111 views

Extend the domain of a function

I get back to a question I post long time ago, because that is quite important to me... Let $\mathbb{X} = \{a, b, c...\}$ be a finite set, $\mathbb{N}$ refers to the set of all natural numbers. I ...
1
vote
1answer
125 views

Difference of 2 notations with powerset

Let $\mathbb{N}, \mathbb{V}$ two sets, $\mathcal{P}(\ldots)$ means the power set of a set. $\mathcal{P}({\mathbb{N}})\rightarrow \mathbb{V}$ can be the type of a function mapping a part of ...
2
votes
1answer
65 views

Define a domain filter of a function

Let $\mathbb{B}, \mathbb{V}$ two sets. I have defined a function $f: \mathbb{B} \rightarrow \mathbb{V}$. $\mathcal{P}(\mathbb{B})$ means the power set of $\mathbb{B}$, I am looking for a function ...
0
votes
1answer
147 views

Naming conventions for super- and subscripts when naming sets and functions

Ok, so say I want to create a bunch of sets and functions for my to-be paper (that surely will get the attention of those comity members in Stockholm), and I want to identify them with the help of ...
9
votes
5answers
527 views

Set {1,1} = Set {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\} = ...
0
votes
1answer
31 views

Notation of instantiating variables by their value in a constraint set

I have a constraint set $C = \{1 \leq x \leq i, j \leq y \leq j+2\}$, now I would like to get another constraint set $C'$ from $C$ to instantiate all $j$ by a value 5, so $C' = \{1 \leq x \leq ...