Proof Inequalities: Find the Solution

  • Thread starter Thread starter phillyolly
  • Start date Start date
  • Tags Tags
    Inequalities Proof
Click For Summary
SUMMARY

The discussion focuses on proving inequalities using the triangle inequality and proof by contradiction. Participants emphasize the importance of identifying when equality holds in the triangle inequality, which is crucial for solving the given problem. The conversation highlights that the initial proof attempt was flawed, indicating a need for a more rigorous approach. Utilizing these methods will lead to a correct solution.

PREREQUISITES
  • Understanding of triangle inequality in mathematics
  • Familiarity with proof by contradiction techniques
  • Basic knowledge of mathematical inequalities
  • Experience with formal proof writing
NEXT STEPS
  • Study the properties of the triangle inequality in depth
  • Learn advanced techniques for proof by contradiction
  • Explore common pitfalls in proving mathematical inequalities
  • Practice writing formal proofs in various mathematical contexts
USEFUL FOR

Students in mathematics, educators teaching proof techniques, and anyone interested in enhancing their skills in formal mathematical reasoning.

phillyolly
Messages
157
Reaction score
0

Homework Statement




The problem and my half solution is given. How do I proceed with the proof?
 

Attachments

  • attempt.jpg
    attempt.jpg
    9.1 KB · Views: 443
Physics news on Phys.org
Try using the triangle inequality. Your proof is flawed.

Or use a proof by contradiction.
 
Last edited:
It is easy to find out when equality holds for the triangle inequality. This is key to your problem.
 

Similar threads

Continuous functions on metric spaces part 2
  • · Replies 8 ·
Replies
8
Views
1K
Help with this inequality needed for a proof in a textbook
  • · Replies 8 ·
Replies
8
Views
1K
Proving well ordering principle from Peano Axioms
  • · Replies 9 ·
Replies
9
Views
2K
Show that the sum of the finite limits of these two series is also finite
  • · Replies 10 ·
Replies
10
Views
2K
Prove inequality of a convex function
  • · Replies 3 ·
Replies
3
Views
1K
How should I show that solutions can be expressed as a Fourier series?
  • · Replies 3 ·
Replies
3
Views
2K
Exploring the Intersection of Ellipsoids and Spherical Shells
  • · Replies 4 ·
Replies
4
Views
2K
How should I show that there exists only one solution?
  • · Replies 11 ·
Replies
11
Views
3K
Proving an Inequality: x+y>=2sqrt(xy)
  • · Replies 6 ·
Replies
6
Views
2K
Proving an integer is composite
  • · Replies 13 ·
Replies
13
Views
1K