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1. Triangle Inequality Let IF be a Pythagorean ordered field. Prove the triangle inequality in the corresponding plane IIF: namely if A,B,C are three pointsin II, then dist (A,C) ≤ dist(A, B) + dist(B,C), and the equality holds if and only if A, B, C are collinear and B is between A and C.

1. Triangle Inequality Let IF be a Pythagorean ordered field. Prove the triangle inequality in the corresponding plane IIF: namely if A,B,C are three pointsin II, then dist (A,C) ≤ dist(A, B) + dist(B,C), and the equality holds if and only if A, B, C are collinear and B is between A and C.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Triangle Inequality Let F be a Pythagorean ordered field. Prove the triangle inequality in the corresponding plane IIF: namely if A,B,C are three pointsin II, then dist(A,C) ≤ dist(A, B) + dist(B,C), and the equality holds if and only if A, B, C are collinear and B is between A and C.
Transcribed Image Text:1. Triangle Inequality Let F be a Pythagorean ordered field. Prove the triangle inequality in the corresponding plane IIF: namely if A,B,C are three pointsin II, then dist(A,C) ≤ dist(A, B) + dist(B,C), and the equality holds if and only if A, B, C are collinear and B is between A and C.
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