What is the difference between a definition and a proof?

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Vol

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What is the difference between a definition and a proof? Is there ever any overlap? :???:
 
Vol said:
What is the difference between a definition and a proof? Is there ever any overlap? :???:
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Direct answer to the overlap question, no.

Do you have particular definitions in mind? Do you have particular theorems that require proof in mind?
 
Vol said:
What is the difference between a definition and a proof? Is there ever any overlap? :???:
Click to expand...
A "definition" defines something. A "proof" proves that some property, behavior, etc, exists, happens, doesn't exist, etc.

For instance, the definition of "circle" might say that it is the locus of points which are some fixed distance "r" from a central point "c". A proof that, say, the set of points (x, y) which are a distance of five units from the point (-3, 4) is a circle would probably use the Distance Formula to show that the set of points complies with the definition, and thus that the set represents a circle. ;)
 
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