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cmurphy
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I need to show that the absolute value of x = max {x, -x}. Of course I know this is true, but I must show this. How would I go about doing such a thing?
Proving the definition of abs. value
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SUMMARY
The absolute value of a real number x is defined as max {x, -x}. This definition is established based on the property that absolute values are always non-negative. The discussion emphasizes that definitions themselves cannot be proved; rather, they serve as foundational statements from which lemmas, theorems, and propositions can be derived. The distinction between proving a definition and proving a theorem is crucial in mathematical discourse.
PREREQUISITES- Understanding of real numbers and their properties
- Familiarity with mathematical definitions and theorems
- Basic knowledge of mathematical proofs and logical reasoning
- Concept of maximum functions in mathematics
- Study the properties of absolute values in real analysis
- Explore the differences between definitions, theorems, and proofs in mathematics
- Learn about lemmas and their role in mathematical arguments
- Investigate the concept of maximum functions and their applications
Mathematics students, educators, and anyone interested in understanding the foundations of mathematical definitions and proofs.
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