Birthdays are anniversaries. Anniversaries are annual activities when we celebrate/honor past events. They do not include the event itself. The first anniversary is 1 year after the initial event.
Yes, that’s the explanation for how we count them as we do, but it has no greater weight (and I’d argue less weight) as to why than saying whether a[0] or a[1] should be the first element in an array.
I say it has less weight as birthday is a compound word, the root words of which suggest that your first birthday could logically be the day of your birth rather than a year after it.
My first weddingday was not a year after I got married. My first graduationday was not a year after I graduated.
Indeed they are, which is why I literally said so in the previous comment. Did you forget to finish reading it?
> They do not include the event itself.
That is true because the event itself is implied information. There is no value in speaking of it. If you stand before us, we can be certain that you had a day of birth (your 0th anniversary). We don't necessarily know how many times you've gone around the sun following that, however, so that is where we find value in communicating additional information.
If you were counting apples, there is the state where you have no apples (index 0), the state where you have one apple (index 1), the state where you have two apples (index 2), etc. When counting you don't need to worry about index 0 because the no apple state is naturally implied. It only becomes interesting and worthy of communication when you have at least one apple to speak of, thus you start at 1. The state found at index 0 is still implicitly there, though.
If no apples is the unusual state, like you expected to find an apple in your lunchbox but someone ate it without your knowledge, then certainly there would be reason to communicate the no apples state. It is ignored in communication when it does not provide useful information, but it is not forgotten. The 0th index is implicitly there.
I say it has less weight as birthday is a compound word, the root words of which suggest that your first birthday could logically be the day of your birth rather than a year after it.
My first weddingday was not a year after I got married. My first graduationday was not a year after I graduated.