"There is a smallest natural number. Exclusion of the lower bound —as in b) and d)— forces for a subsequence starting at the smallest natural number the lower bound as mentioned into the realm of the unnatural numbers. That is ugly, so for the lower bound we prefer the ≤ as in a) and c). Consider now the subsequences starting at the smallest natural number: inclusion of the upper bound would then force the latter to be unnatural by the time the sequence has shrunk to the empty one. That is ugly, so for the upper bound we prefer < as in a) and d). We conclude that convention a) is to be preferred."
I mean... that doesn't exactly settle it. Sure, your opinion might coincide with that, but this is not a logical argument. First you're going to have to explain what unnatural numbers are (because they're not a thing as far as I can tell), and then you'll have to tell me what about them makes them "ugly", and how that makes the other option "preferable".