# Tagged Questions

For questions about approaches and techniques for discovering a proof, as opposed to writing it down clearly (which involves (proof-writing)). Should not be used unless the focus is on the technique of the proof instead of the solution.

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So I have $\cdot \lim \limits_{n \to \infty} \sqrt{n^2+1} -n$ I understand that the limit is 0 because, $$\cdot \lim \limits_{n \to \infty} \sqrt{n^2+1} -n = \left(\sqrt{n^2+1}-n ... 2answers 33 views ### Prove 3 \mid x-2 \implies 3 \mid (x^2 - x+1) using division algorithm I can't figure out how to prove the following implication using the division algorithm:$$3 \mid x-2 \implies 3 \mid (x^2 - x+1)$$It seems simple enough. Does anyone know how? 1answer 34 views ### How many solutions does x(1 - 1000m) + y (10 - 100m) + z (100-10m) + w(1000-m) = 0 restricted to some constraints Consider the linear equation:$$x(1 - 1000m) + y (10 - 100m) + z (100-10m) + w(1000-m) = 0 \qquad (1) where $x,y,z,w \in \mathbb N_9, \; xw \neq 0, m \in \{ 2,3,\dots, 9 \}$ Having put this to a ...
I'm trying to prove the Monotone Convergence Theorem for decreasing sequences, namely if Let $(X,\mathcal{M},\mu)$ be a measure space and suppose $\{f_n\}$ are non-negative measurable functions ...