0
votes
0answers
20 views

Produce a list of the most-similar units, given various correlations/relationships

I have a database full of units (U1 - U50, U51...) where every unit has the same standard attributes (A1 - A10) and where a % of each attribute defines the amount of that attribute for that particular ...
0
votes
1answer
52 views

Question about posets and maxima/minima

A thought just occurred to me, thinking about posets and maxima/minima... This is a "little" question just to make sure I am really grasping the definitions here: if $E$ is partially ordered by a ...
1
vote
1answer
31 views

Relation between two gamma functions

Does anyone know the relation between these two gamma functions? 1st) Gamma[1 + c, a (1 + b)] 2nd) Gamma[c, a (1 + b)] The question is: may I write the 1st like the 2nd times something? thank you ...
1
vote
0answers
100 views

Prove that for any $W\in Q$, there exist a bijection $f:[0]\to W$

Suppose $R$ be the relation on $[0,1)$ s.t. $aRb\iff a-b$ is rational. Let $[0]$ be the equivalence class with respect to relation $R$ on $[0,1)$. Let $Q$ be the set of all equivalence class on [0,1). ...
1
vote
1answer
100 views

Total Ordering and relation

Consider the relation $<$ on $\mathbb{Q}$ defined by: $(m, n) < (j, k) \iff jn-mk \in \mathbb{N}.$ Where $m, j \in \mathbb{N}$ and $n, k\in\mathbb{Z}$ I want to show that $<$ is a total ...
2
votes
3answers
210 views

Why is 'Antisymmetry' named so?

So when we talk about order relations for the familiar number systems, we are always introduced to the antisymmetry property which is $x \le y, x \ge y \implies x=y$. When I think of the word ...
7
votes
5answers
691 views

Dependence of Axioms of Equivalence Relation?

This question is problem 11(a) in chapter 1 in 'Topics in Algebra' by I.N. Herstein. These are the properties of equivalence relation given in this book. Prop 1 $a \sim a$ Prop 2 $a \sim b$ ...