# Omega

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# 123 Posts

 Apr2 asked Using Gauss-Jordan for an infinite-solutions system Apr2 asked Are there no solutions for $\begin {cases} 2x+4y = 6\\ 3x+6y = 5\end {cases}$? Apr2 asked Can all equation systems be reduced to the identity matrix? Apr1 asked Recurrence relation to calculate the number of strings of $n$ characters that don't have consecutive vowels. Mar27 asked How to get the characteristic equation from a recurrence relation of this form? Dec5 asked Advice for proving with induction scenarios with multiple chances for using the hypothesis. Dec5 asked Finding the explicit formula for the succession $x_0=2, x_{n+1} = 5x_n$ and proving it with induction Dec5 asked Proving $\frac{(n+1)^4}{4}+(n+1)^3\le\frac{(n+2)^4}{4}$ for all $n \ge 1$. Dec3 asked Proving by induction that $n(n+1)(n+2)$ is divisible by $6$ for all $n \ge 1$ Dec3 asked Proving by induction inequalities that lack the variable on the right side. 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 asked What is the purpose of the first test in an inductive proof? Nov9 asked Proving that $f(n,m) = 3^n5^m$ is injective. Nov9 asked Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$ Nov9 asked If $f$ is injective, demonstrate that $f \circ g = f \circ h \implies g = h$ 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? 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.