Talk:Gibbs' inequality
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The proof on this page seems to state that 
. However, I was defined so that pi = 0 whenever 
, so making this change in the indices for the sum introduces indeterminate terms of the form 
.
Changing the indices for the sum may introduce similar indeterminate forms on the left hand side of that inequality, as well.
How can this proof be corrected?
- The notation used on this page is lazy. The implicit understanding is that a new function is defined as:
- but the author (me - reetep) didn't bother to specify this explicitly. My apologies - it's the sort of thing you do without thinking after having completed a mathematics degree; you become accustomed to writing mathematics for people with a similar background in maths and more often than not you find yourself demonstrating how something might be proved without actually doing it (because you have neglected to complete all of the technical details).
If you refer to the definition of mathematical entropy you should find there that a similar definition has been made for the log function. This is essentially what Gibbs' inequality is about and we are talking about the same function in this article.
