I answered:> 1. If you are willing to wait an infinite amount of time, I think the
> minimum fee will always be zero or very close to zero, so I think it's a
> silly question.That's not what I'm thinking. It is just an observation based on the fact that blocks are found at random intervals.
Every once in a while the network will get lucky and we'll find six blocks in ten minutes. If you are deciding what transaction fee to put on your transaction, and you're willing to wait until that six-blocks-in-ten-minutes once-a-week event, submit your transaction with a low fee.
All the higher-fee transactions waiting to be confirmed will get confirmed in the first five blocks and, if miners don't have any floor on the fee they'll accept (they will, but lets pretend they won't) then your very-low-fee transaction will get confirmed.