Note (return) — Chapter V

"The word infinite, therefore, in mathematical usage, as applied to process and to quantity, has a two-fold signification. An infinite process is one which we can continue as long as we please, but which exists solely in our continuance of it. 221 An infinite quantity is one which exceeds our powers of mensuration or of conception, but which, nevertheless, has bounds and limits in itself. 222 Hence the possibility of relation among infinite quantities, and of different orders of infinities. If the words infinite, infinity, infinitesimal, should be banished from mathematical treatises and replaced by the words indefinite, indefinity, and indefinitesimal, mathematics would suffer no loss, while, by removing a perpetual source of confusion, metaphysics would get great gain."