query: How to start proof of triangular inequality?
positive_passages.docid: 27954
positive_passages.text: Prove triangle inequality using the properties of absolute value
negative_passages.docid: 30044
negative_passages.text: Inequality with triangle sides
negative_passages.docid: 8207
negative_passages.text: Can I prove this inequality algebraically?
negative_passages.docid: 88687
negative_passages.text: Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
negative_passages.docid: 77026
negative_passages.text: Proof with inequalities
negative_passages.docid: 30386
negative_passages.text: Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
negative_passages.docid: 3030
negative_passages.text: Proving inequality $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3\sqrt[3]{abc}}{a+b+c} \geq 4$
negative_passages.docid: 138036
negative_passages.text: Proving Inequality using Induction $a^n-b^n \leq na^{n-1}(a-b)$
negative_passages.docid: 142785
negative_passages.text: How can I prove Holder inequality for $0<p<1$?
negative_passages.docid: 147785
negative_passages.text: Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
negative_passages.docid: 27272
negative_passages.text: Triangle Inequality with Complex Numbers
negative_passages.docid: 24617
negative_passages.text: Proof of Inequality using AM-GM
negative_passages.docid: 67851
negative_passages.text: Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?
negative_passages.docid: 115335
negative_passages.text: How can we prove this integral inequality?
negative_passages.docid: 5369
negative_passages.text: Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
negative_passages.docid: 39015
negative_passages.text: Prove the triangle inequality on the sphere $S^2$ in $\mathbb{R}^3$.
negative_passages.docid: 150609
negative_passages.text: Triangle Inequality of the Cartesian product with Max function