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People go about understanding mathematical definitions in different ways; the steps they take may vary. Here's one way:
Step 1. | Read the definition more than once. |
Step 2. | Identify what "things" the definition is talking about. |
Step 3. | Generate a test case. |
Step 4. | Determine if the example fits the definition. |
Step 5. | Find examples that do not fit the definition. |
Step 6. | Try to generalize the examples to create an image of the full concept. (In the case of convex figures, you might think about curved figures, three-dimensional figures, etc.) |
Convex, like many other mathematical ideas, has several different, but equivalent definitions. Not every proposed definition will work, though, and some definitions are better than others -- they may be more clear, use fewer words, or be easier to test.
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