- #1
crocomut
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How do we show that 2.2.19 and 2.3.21 are equal in this textbook?
- Context: Graduate
- Thread starter crocomut
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SUMMARY
In the discussion, users clarify that the equality of 2.2.19 and 2.3.21 in the textbook can be demonstrated by swapping dummy indices i and j. This standard trick maintains the integrity of the expression. Following this, adding the two expressions and dividing by 2 confirms their equivalence. This method is a common technique in mathematical proofs involving dummy variables.
PREREQUISITES- Understanding of dummy indices in mathematical expressions
- Familiarity with basic algebraic manipulation
- Knowledge of mathematical proofs and equivalences
- Experience with textbook problem-solving techniques
- Research techniques for manipulating dummy variables in proofs
- Explore algebraic methods for proving expression equivalence
- Learn about common mathematical tricks used in textbooks
- Review examples of similar problems in mathematical literature
Students, educators, and anyone involved in mathematical problem-solving who seeks to understand techniques for proving expression equivalence in textbooks.
- #2
tiny-tim
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hi crocomut! 
standard trick:
swap i and j … since they're both dummy indices, that gives you the same expression!
standard trick:
swap i and j … since they're both dummy indices, that gives you the same expression!
then add, and divide by 2 
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