- #1
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- Homework Statement
- I'm trying to come up with ways to find a continuous
such that and with .
- Relevant Equations
- My understanding of this problem is a bit infantile. I want some math veterans to haze my poor understanding into shape.
Let be a continuous function defined in . is the standard Euclidean metric. Then here are my suggested ways to choose :
1. Choose any continuous that satisfies
because the inequality ensures with . Can you think of any specific examples?
2. Choose any continuous that satisfies and A simple example would be .
Thank you.
edit: continuous
Also, I'm wondering if category 1 is invalid, i.e., if there do not exist functions that meet category 1.
1. Choose any continuous
2. Choose any continuous
Thank you.
edit: continuous
Also, I'm wondering if category 1 is invalid, i.e., if there do not exist functions that meet category 1.
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