When Shakespeare’s Enobarbus said of Cleopatra that “age cannot wither her, nor custom stale her infinite variety,” he was obviously exaggerating. So few are the literal uses of “infinite” that almost every use of it is metaphorical. There is not an infinite number of possible positions on a chessboard, nor number of stars in the known universe. Things can be innumerable (in one sense of the word) without being infinite; in other words, things which are beyond the human capacity to count can still be limited in number.
“Infinite” has its uses as a loose synonym for “a very great many,” but it is all too often lazily used when one doesn’t want to do the work to discover the order of magnitude involved. When you are making quasi-scientific statements you do a disservice to your reader by implying infinity when mere billions are involved.
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