query: Verifying that $d(x,y)= \sum_{i=1}^n (x-y)^2%$ satisfies the triangle inequality
positive_passages.docid: 23203
positive_passages.text: Euclidean distance proof
negative_passages.docid: 88956
negative_passages.text: For any three vectors $x,y,z\in\mathbb{R}^d$, we have $ \|y-z\|\cdot\|x\|\leq\|x-y\|\cdot\|z\|+\|z-x\|\cdot\|y\|$
negative_passages.docid: 98921
negative_passages.text: Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
negative_passages.docid: 125175
negative_passages.text: convexity proof of a function including ln and sums
negative_passages.docid: 24617
negative_passages.text: Proof of Inequality using AM-GM
negative_passages.docid: 20863
negative_passages.text: how do I prove this inequallity?
negative_passages.docid: 36374
negative_passages.text: Exercise 1.6.3 from Alon & Spencer's *The Probabilistic Method*: prove that $Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1]$ for i.i.d. real RVs $X$ and $Y$
negative_passages.docid: 8207
negative_passages.text: Can I prove this inequality algebraically?
negative_passages.docid: 1305
negative_passages.text: Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
negative_passages.docid: 77464
negative_passages.text: Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact
negative_passages.docid: 27901
negative_passages.text: Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$
negative_passages.docid: 124968
negative_passages.text: How prove this inequality $\sum\limits_{cyc}\frac{x+y}{\sqrt{x^2+xy+y^2+yz}}\ge 2+\sqrt{\frac{xy+yz+xz}{x^2+y^2+z^2}}$
negative_passages.docid: 68986
negative_passages.text: Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
negative_passages.docid: 140857
negative_passages.text: Using Bernoulli's Inequality to prove an inequality
negative_passages.docid: 7775
negative_passages.text: Show that $|x-y|\leq |x|+|y|$.
negative_passages.docid: 155341
negative_passages.text: Proving or disproving inequality $ \frac{xy}{z} + \frac{yz}{x} + \frac{zx}{y} \ge x + y + z $
negative_passages.docid: 77134
negative_passages.text: Proving a three variables inequality