Some trouble understanding this basic inequality proof

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  • Thread starter Thread starter Terrell
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    Inequality Proof
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SUMMARY

The discussion centers on understanding the basic proof of the inequality involving factorials, specifically demonstrating that (n+1)! equals (n+1) multiplied by n factorial (n!). The user initially struggled with the manipulation of the inequality but ultimately clarified that (n+1)! can be expressed as (n+1) * n * (n-1) * ... * 1. This highlights the importance of recognizing factorial definitions in mathematical proofs.

PREREQUISITES
  • Understanding of factorial notation and operations
  • Basic knowledge of mathematical inequalities
  • Familiarity with proof techniques in mathematics
  • Concept of mathematical induction
NEXT STEPS
  • Study the properties of factorials and their applications in combinatorics
  • Learn about mathematical induction and its role in proving inequalities
  • Explore advanced proof techniques such as contradiction and contrapositive
  • Investigate common inequalities in mathematics, such as the AM-GM inequality
USEFUL FOR

Students beginning their journey in mathematical proofs, educators teaching proof techniques, and anyone looking to strengthen their understanding of factorials and inequalities.

Terrell
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just starting out with proofs... i tried manipulating the right side of the inequality, but i don't see why it's equal to (n+1)!
 

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oh nevermind. i got it. (n+1)! = (n+1)*n*(n-1)*...
 

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