Hmm you're right it's no more rigorous what I said. (For each positive number the expression must eventually, after finitely many terms, always be smaller than that number thereafter)
But you're not right in that the upper bound of that expression eventually stops decreasing, in fact for simple f and g as long as f is positive and eventually bounded by g the expression will decrease infinitely often if my intuition is correct
> you need to spend more than one defensive missile per attacking missile, because you might miss
It's almost always the case that you'll expend more than one interceptor per incoming missile as interception is probabilistic. In general, you can estimate the number of missiles you'll need to achieve a certain probability of interception with the following formula: 1 - (1.0 - sspk)^n, where sspk is the single shot probability of kill (i.e., successful interception with a single interceptor) and n is the number of interceptors.
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