# Omega

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 Nov7 comment Determining equivalence classes of certain pairs for the relation $(a,b)R(c,d) \iff a^2 + 7b^2 = c^2 +7d^2$ Just to be clear: if $d = 2$, then $7d^2 = 28$, so we would need $c^2 = -20$. However, we can't have a $c$ that fulfils $c^2 = -20$ right? So I guess it's not possible to have $d > 1$? Nov7 asked Determining equivalence classes of certain pairs for the relation $(a,b)R(c,d) \iff a^2 + 7b^2 = c^2 +7d^2$ Nov7 accepted Finding order properties in the relation $aSb \iff \exists k \in \mathbb{N} : b = ak$ Nov7 revised Finding order properties in the relation $aSb \iff \exists k \in \mathbb{N} : b = ak$ deleted 3 characters in body Nov7 asked Finding order properties in the relation $aSb \iff \exists k \in \mathbb{N} : b = ak$ Nov7 accepted What is the equivalence class of a relation's element? Nov7 revised Determining the properties for the relation over $P(\mathbb{N})$ where $ARB \iff A \cup B \in H$ added 75 characters in body Nov7 comment Determining the properties for the relation over $P(\mathbb{N})$ where $ARB \iff A \cup B \in H$ $A = \{1,2,3\}$ and $B = \mathbb{N}$, $A$ is not reflexive, $ARB$ holds since $\overline{B}$ is finite - but I still don't see how does that serve as a counterexample for transitivity. Nov7 asked Determining the properties for the relation over $P(\mathbb{N})$ where $ARB \iff A \cup B \in H$ Nov7 asked What is the equivalence class of a relation's element? Nov7 comment Finding the first, last, minimal and maximal elements in these relations. @dfeuer: Just to be clear, what is your definition of "a set's class"? Nov7 comment Finding the first, last, minimal and maximal elements in these relations. @dfeuer: Without actually knowing their contents? I'm afraid not....... Unless.... Maybe, wouldn't it be $\emptyset$ in this case? Since $\emptyset \subseteq whateverSet$? Nov7 asked Finding the first, last, minimal and maximal elements in these relations. Nov6 accepted How can I determine that a relation lacks a property without using a counterexample? Nov6 comment Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$? If a relation used single elements, would a metric line be a good analogy...? Nov6 comment Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$? Daaaaamn. Back to scratch. I really like the graph idea, I wonder if I could use that more often for the other relations I tried. Nov6 accepted Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$? Nov6 asked Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$? Nov6 asked How can I determine that a relation lacks a property without using a counterexample? Nov6 accepted Properties of relation $R$ on $\mathbb{N} \times \mathbb{N}:\;(a,b)R(c,d) \iff a -c = b -d$