(…) and they were getting stronger with/for every day
What's the difference/the correct one to use?
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(…) and they were getting stronger with every day
With is correct here because it indicates the "getting stronger" and the "every day" are occurring simultaneously, or with each other. For is incorrect here because it would indicate that whoever/whatever is getting stronger is doing for the purpose of "every day," which is nonsensical.
However, the preposition could be dropped altogether with no loss of meaning:
(…) and they were getting stronger every day