# Tagged Questions

15 views

### Difference between Inclusion and continuation

Halmos defines the order continuation as follows: We shall say that a well ordered set A is a continuation of well ordered set B if B is a subset of A, if, in fact, B is an intial segment of A and ...
29 views

### How is a relation defined on ordered sets?

I am reading that $(\mathbb{Z}, \leq )$ is a total ordered set. I understand how it satisfies reflexivity, antisymmetry, transitivity. But it says that because for any $a,b \in \mathbb{Z}$, either ...
45 views

23 views

### Prove that R is an equivalence relation on F

A relation $R$ is defined on the set $F = \{f: \Bbb R \to \Bbb R\}$ $$fRg \iff f(0) = g(0).$$ My approach: This is reflexive because: $f(0) = f(0)$ is same as $f(0) = g(0)$ This is symmetric ...
91 views

### Determine if R is an equivalence relation

I've got this question: Consider the relationship $R$ between ordered pairs of natural numbers such that $(a, b)$ is related to $(c, d)$ (denoted by $(a, b) R (c, d)$) if and only if $ad = bc$. ...
My book says that a relation R on A is reflexive, if $\ (a,a) \in R, \ for\ every \ a \in A$ symmetric, if $\ (a_1,a_2) \in R \implies (a_2,a_1) \in R,\ for\ all\ a_1,a_2 \in A$ Although I ...
Suppose I have the following relation $$R = \{(1,1), (2,3), (3,1)\}$$ To make it reflexive we add the following missing pairs: $$\{(2,2), (3,3)\}$$ Now I wonder how to find the reflexive transitive ...