# Omega

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# 94 Accepts

 Dec3 accepted Proving by induction that $1+\frac{1}{2}+\frac{1}{3}+…+\frac{1}{n}\le\frac{n}{2}+1$ holds for all $n \ge 1$ Dec1 accepted What is the purpose of the first test in an inductive proof? Nov9 accepted Determining the properties for the relation over $P(\mathbb{N})$ where $ARB \iff A \cup B \in H$ Nov9 accepted If $f$ is injective, demonstrate that $f \circ g = f \circ h \implies g = h$ Nov9 accepted Demonstrating that $f(x) = x^2 + 1$ is bijective and calculating $f \circ f^{-1}(x)$ Nov9 accepted Functions exercise for $f(x) = \begin{cases} x \textrm{ if } x \le 3 \\ 11 - 2x \textrm{ if } 3 < x\end{cases}$ Nov8 accepted 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 accepted 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? Nov6 accepted How can I determine that a relation lacks a property without using a counterexample? 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 accepted Properties of relation $R$ on $\mathbb{N} \times \mathbb{N}:\;(a,b)R(c,d) \iff a -c = b -d$ Nov5 accepted Is this equation to prove that $aRb \iff a^2 - b^2 = 1$ is antisymmetric correct? Nov5 accepted Proving a relation's inverse's properties by knowing the original's. Nov4 accepted How can I further simplify $(a \le b) \lor (b \le a)$ to prove that it is a tautology? Nov3 accepted Proving that $R$ is antisymmetric if and only if $G \cap G^{-1} \subseteq D$ Sep29 accepted Determining $A \triangle B = B - C \implies A \subseteq B$ Sep28 accepted How do I determine cardinalities, given the cardinality of other sets? Sep28 accepted Determining $(X \cap Y \subseteq \overline{A} \land Y \subseteq B) \implies Y \subseteq B - A$