query: Prove the triangle inequality |z+w|≤|z|+|w| where z ∈C, w ∈C
positive_passages.docid: 27272
positive_passages.text: Triangle Inequality with Complex Numbers
negative_passages.docid: 125817
negative_passages.text: show this inequality $(x+y)^3+(y+z)^3+(z+w)^3+(w+x)^3\ge 8(x^2y+y^2z+z^2w+w^2x)$
negative_passages.docid: 117281
negative_passages.text: How prove this inequality $x^3y+y^3z+z^3x\ge xyz(x+y+z)$
negative_passages.docid: 106979
negative_passages.text: Prove the inequality and limitation
negative_passages.docid: 89170
negative_passages.text: How prove this inequality $\frac{x^2y}{z}+\frac{y^2z}{x}+\frac{z^2x}{y}\ge x^2+y^2+z^2$
negative_passages.docid: 91662
negative_passages.text: Proof for triangle inequality for vectors
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: 56101
negative_passages.text: Prove the inequality $\frac{a}{c+a-b}+\frac{b}{a+b-c}+\frac{c}{b+c-a}\ge{3}$
negative_passages.docid: 79491
negative_passages.text: Inequality $(a+b)^2 + (a+b+4c)^2\ge \frac{kabc}{a+b+c}$ for $a,b,c \in\mathbb{R}$
negative_passages.docid: 19804
negative_passages.text: How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
negative_passages.docid: 77576
negative_passages.text: Using the triangle inequalities to prove a bound in the complex plane
negative_passages.docid: 15237
negative_passages.text: Prove an inequality using complex analysis
negative_passages.docid: 30044
negative_passages.text: Inequality with triangle sides
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality
negative_passages.docid: 126632
negative_passages.text: Proving Inequalities with Absolute values
negative_passages.docid: 104217
negative_passages.text: Alternative triangle inequality proof
negative_passages.docid: 66707
negative_passages.text: How to prove this inequality? $ | z-1 | \le | | z | -1 | + | z| \cdot | \arg z | $