I've implement a few string search algorithms and translating between 1- and 0- based offset functions was the source of a huge number of bugs, as you might expect. For some reason a lot of sources present the algorithms as 1-based.
Because that's a natural mathematical model. "the n-th element" being at position n is handy and natural. What's nuts is that array indexing based on pointer offsets has made its way into nearly all high-level languages.
On an infinite tape, there is no "first byte", only "a byte placed where the tape already was when you started" (i.e. at offset=0.)
Similarly, there is no "first byte" of a random-access memory, because the ordering of memory is not guaranteed (i.e. some memories have bit-planes, some memories have banks, some memories are big/little-endian, etc.) The only thing you can say about a memory (and thereby about a RAM-word machine, or about an array) is what exists at address 0 of it, at address 1 of it, etc. It would be incorrect to describe address 0 as "the first byte" of memory, as this would impose a canonical iteration order.
Maybe, but human brain likes things starting at 1.
No it's not; it's a artifact of humans numbering items based on "total I have, including this one" rather than the more sensible but contrary to a implementation detail of human neuropsychology "number of items preceeding this one".
> "the n-th element" being at position n is handy and natural.
Yes, starting with the 0th element at position 0.