For a site to be marked as a homepage it must be a named an index when saving it and making a webpage. Historically this was implemented because if there wasn't an index address then the page was listing all the directory contents.
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Each web server has a directory. Index htm or index html is the default page name in that directory. The main page or homepage should have the extension index htm.
A home page is the website you choose to see everytime you open Internet Explorer and is the website that will appear each time you click the house on the Internet Explorer Browser toolbar. (Note this may be different for Internet Explorer 7)
Bond's work index one of the most acceptable approach to calculate the grindability index.
And index is in the back of a story or book.
i is a short for index, as far as I know. I think it also comes from math, where you have i as an index (also j,k,l,...) for Sigma, a summary of a general series item. In a programming language called Jovial, using i (or any other one letter index) will generate a faster code than using loopCounter, index, or any other name for the loop counter which is longer than one letter. It uses a register if you use a one letter variable, but I'm pretty sure that is not the case in common languages such as C.