All Questions
Tagged with magma elementary-set-theory
4
questions
4
votes
1
answer
55
views
How many different operations can be defined in a finite groupoid with a given property?
Set $B=\left\{ 1, 2, ... 18 \right\}$ is given. How many different operations $*$ can be defined so that $(B,*)$ is a groupoid with a property that $|\left\{i|i*(19-i) \neq i ∧ i*(19-i) \neq (19-i)\...
- 455
3
votes
1
answer
114
views
Name for the property of “being a Cartesian product of arbitrary sets”
Suppose I have a set $S$ of pairs (or, in general, tuples, or objects with two or more parts/attributes/projections). This set may have the property that
$$(a, b) \in S \wedge (a', b') \in S \...
- 988
2
votes
2
answers
94
views
Sets as extremely trivial groups
A group is a structure defined upon an underlying set which is endowed with a single binary operator that has some rules attached to it. I was wondering whether one could describe a set itself as ...
- 35
1
vote
1
answer
3k
views
Proving that $f(A+B)=f(A)+f(B).$
Let $X$ and $Y$ denote magmas, and suppose $f : X \rightarrow Y$ is homomorphism. Then I think that for all $A,B \subseteq X$, we have $f(A+B)=f(A)+f(B).$ However, I'm not happy with my:
Proof. The ...
- 68.1k