1.20 (b) Baby Rudin: $y-x>0 \rightarrow \exists n \, n(y-x)>1$ short question
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Baby Rudin Theorem 1.20 (b) Proof
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$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
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$Y=\prod_{n\in\mathbb{N}}X$.
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Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
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Prove $(x+y) \text{ mod } n = ((x \text{ mod } n)+(y \text{ mod } n)) \text{ mod } n,\,$ and product analog
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Criteria for convergent sequence (Baby Rudin Theorem 3.22)
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Prove that $x^y < y^x$
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How to show that $\vdash (\forall x \beta \to \alpha) \leftrightarrow \exists x (\beta \to \alpha)$?
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How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
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Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
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How to verify whether or not there exists a vector $x$ such that $Ax > 0$?
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Supremum of the infimum
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Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
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Can we find $c_n$ to make $X_nc_n \rightarrow 0$ almost surely, even if $EX_n > \infty$?
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Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
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Show that $\exists c \in \mathbb{R} : f(c) = 0$
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Are positive real numbers $x,y$ allowed to be taken out during this proof?