INFINITELY
This word, like infiniment in French, is commonly used for 'extremely', and it is pedantic to object to it by insisting always on its full logical meaning; but it should be avoided where measurable quantities are spoken of; for instance, one may say to indoctrinate the mob with philosophical notions does infinite harm, but to say that England is infinitely more populous than Australia is absurd. That one can rightly call atoms infinitely small means that they are to our senses immeasurable, and the word, as it here carries wonder, may, like other conversational expletives, have an emotional force, and can therefore be sometimes well used even where its exaggeration is apparent. As when a man heightens some assertion with a 'damnable,' he intends by the colour of his speech to warn you that his conviction is profound, and that he is in no mood to listen to reason, so the exaggeration of 'infinite' may have special value by giving emotional colour to a sentence.
On the above principles there will be doubtful cases. For instance, was Mr. Lloyd George justified the other day in saying, If you cut down expenditure to the lowest possible limit, the war debt would still be so enormous that … the expenditure for this country is bound to be infinitely greater than before the war?—The Times, Oct. 23.