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Nov
7
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 $d > 1$?
Nov
7
asked Determining equivalence classes of certain pairs for the relation $(a,b)R(c,d) \iff a^2 + 7b^2 = c^2 +7d^2$
Nov
7
accepted Finding order properties in the relation $aSb \iff \exists k \in \mathbb{N} : b = ak$
Nov
7
revised Finding order properties in the relation $aSb \iff \exists k \in \mathbb{N} : b = ak$
deleted 3 characters in body
Nov
7
asked Finding order properties in the relation $aSb \iff \exists k \in \mathbb{N} : b = ak$
Nov
7
accepted What is the equivalence class of a relation's element?
Nov
7
revised Determining the properties for the relation over $P(\mathbb{N})$ where $ARB \iff A \cup B \in H$
added 75 characters in body
Nov
7
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.
Nov
7
asked Determining the properties for the relation over $P(\mathbb{N})$ where $ARB \iff A \cup B \in H$
Nov
7
asked What is the equivalence class of a relation's element?
Nov
7
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"?
Nov
7
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 $\emptyset \subseteq whateverSet$?
Nov
7
asked Finding the first, last, minimal and maximal elements in these relations.
Nov
6
accepted How can I determine that a relation lacks a property without using a counterexample?
Nov
6
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...?
Nov
6
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.
Nov
6
accepted Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$?
Nov
6
asked Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$?
Nov
6
asked How can I determine that a relation lacks a property without using a counterexample?
Nov
6
accepted Properties of relation $R$ on $\mathbb{N} \times \mathbb{N}:\;(a,b)R(c,d) \iff a -c = b -d$