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Why, in functional analysis, is so important to calculate best constant in an embedding inequality?

Cross-posted to :"http://mathoverflow.net/questions/161483/understanding-reasons-for-best-constants-in-inequalities".

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Why do we want a job with the highest salary? –  vadim123 Mar 26 at 14:39
    
I don't get the sarcasm; the more I get paid the more I can eat, while finding the best constant doesn't give anything! –  Felice Iandoli Mar 26 at 14:41
    
It's not sarcasm. Even if you make enough to fill your belly you still want more money. –  vadim123 Mar 26 at 14:53

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