# Omega

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 Dec3 asked Proving by induction inequalities that lack the variable on the right side. Dec3 comment Proving by induction that $1+\frac{1}{2}+\frac{1}{3}+…+\frac{1}{n}\le\frac{n}{2}+1$ holds for all $n \ge 1$ @TenaliRaman: I know what they did, I don't know why, of all options, they had to choose that one. They could've added something else to both sides too, right? Why not? Dec3 accepted Proving by induction that $1+\frac{1}{2}+\frac{1}{3}+…+\frac{1}{n}\le\frac{n}{2}+1$ holds for all $n \ge 1$ Dec3 asked Proving by induction that $1+\frac{1}{2}+\frac{1}{3}+…+\frac{1}{n}\le\frac{n}{2}+1$ holds for all $n \ge 1$ Dec2 asked Proving by induction that $\sum_{i=2}^n(i^2-i) = \frac{n(n^2-1)}{3}$ for all $n \ge 2$ Dec1 awarded Nice Question Dec1 accepted What is the purpose of the first test in an inductive proof? Dec1 asked What is the purpose of the first test in an inductive proof? Nov9 comment Proving that $f(n,m) = 3^n5^m$ is injective. @AymanHourieh: Of couurseeee.. No, I fear not. I will check it out, thank you. Nov9 asked Proving that $f(n,m) = 3^n5^m$ is injective. Nov9 accepted Determining the properties for the relation over $P(\mathbb{N})$ where $ARB \iff A \cup B \in H$ Nov9 asked Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$ Nov9 accepted If $f$ is injective, demonstrate that $f \circ g = f \circ h \implies g = h$ Nov9 comment If $f$ is injective, demonstrate that $f \circ g = f \circ h \implies g = h$ Wait, what is the contradiction? Plus, in what part did you apply the fact that $f$ is injective? Nov9 asked 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 comment How to work with function properties when it is defined by an equation system? I see. Thanks! That should be an answer. Nov9 asked Demonstrating that $f(x) = x^2 + 1$ is bijective and calculating $f \circ f^{-1}(x)$ Nov9 asked How to work with function properties when it is defined by an equation system? Nov9 accepted Functions exercise for $f(x) = \begin{cases} x \textrm{ if } x \le 3 \\ 11 - 2x \textrm{ if } 3 < x\end{cases}$