# Tagged Questions

If you already have a proof for some result, but want to ask for a different proof (using different methods).

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### Show that a piecewise function of two solutions to an ODE is a solution to the ODE

Let $x=x(t)$. If the first order ODE $x'=f(t,x) (*)$ is satisfied by $u$ and $v$, each over $I = (a,b)$, show that $$w(t) := u1_{(a,t_0)} + v1_{[t_0,b)}$$ satisfies $(*)$, where $u(t_0) = v(t_0)$ ...
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### Show code $C$ is a 1 error correcting

Let $C=\{(0,0,0,0,0),(1,1,1,0,0),(0,0,1,1,1),(1,1,0,1,1)\}\in\mathbb{F}_2$. Show $C$ is $1$ error correcting. Definition: a code $C\subseteq\mathbb{F}^n$ is t error correcting , if for any two ...
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### Proof using pumping lemma that $\{0^m1^n \mid m \neq n \}$ is not regular

First of all, there's already a question very similar to this, but in my case I just wanted to show my attempt with the hope that if there are any erros or it's wrong completely you can help me in the ...
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### Proof for $\frac{2}{\pi}x \lt \sin{x}$ for $x \in (0,\frac{\pi}2)$

The following is part of exercise 6.26.21 from Tom Apostol's Calculus Volume 1. I wonder if my proof is correct and if there is a simpler alternative proof. Prove the following by examining the ...