It is also frequently called the tombstone . G. P. Hochschild worked with Halmos at the University of Chicago, and on hearing that Halmos was writing a book asked if his name would be in the book. The reference was to the index page itself, a genuine self-referential index. Here is the story in his own words from his autobiography, I Want to be a Mathematician . My most nearly immortal contributions are an abbreviation and a typographical symbol.
Infinity is the negated form of the Latin word finire for limited, bounded, or finished.
Infinite then would literally mean that which is unlimited or unbounded. Originally only used to apply to things that were unmeasureably large, the origin of theories of limits led to the need for a word that expressed the idea of things growing smaller and smaller without bound. Why he used it seems lost to history. The two most popular suggestions are these. Since Wallis was a classical scholar, this may have been one source.