# Omega

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bio website location age 19 member for 3 years, 2 months seen Mar 8 at 0:40 profile views 170

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 Nov8 comment Functions exercise for $f(x) = \begin{cases} x \textrm{ if } x \le 3 \\ 11 - 2x \textrm{ if } 3 < x\end{cases}$ Oh snap. Thanks for the observations! Nov8 asked Functions exercise for $f(x) = \begin{cases} x \textrm{ if } x \le 3 \\ 11 - 2x \textrm{ if } 3 < x\end{cases}$ Nov8 asked Proving that the relation $(x,y)S(x',y') \iff x - x' \in \mathbb{Z} \land y = y'$ is of equivalence. Nov8 comment How to determine the equivalence classes of a relation? Thanks! Why $\phi^{-1}(\{k\})$ and not $\phi^{-1}(k)$ by the way? Nov8 accepted How to determine the equivalence classes of a relation? Nov8 comment How to determine the equivalence classes of a relation? Could you elaborate more on what happened at "$\phi^{-1} ( \{ k \} )$ for $k = 0,1,2$"? I'm a little bit lost there. Nov8 asked How to determine the equivalence classes of a relation? Nov7 accepted Determining equivalence classes of certain pairs for the relation $(a,b)R(c,d) \iff a^2 + 7b^2 = c^2 +7d^2$ 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 $\emptyset \subseteq whateverSet$?