Let $x$ and $y$ be unique real numbers. How do you prove that there exists a neighborhood $P$ of $x$ and a neighborhood $Q$ of $y$ such that $P \cap Q = \emptyset$?
Finding disjoint neighborhoods of two points in $\Bbb R$
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calculus
real-analysis
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2**Hint:** Consider $d = \dfrac{|x - y|}{2}$. – 2012-09-03
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0One usually writes "Let $x$ and $y$ be distinct real numbers." – 2012-09-04