Looking at a Prefix/Suffix chart confirms that the prefix "in-" is supposed to mean 'not' or 'without', just wondering why the exception only occurs for certain words. I don't know if it's an origin thing, as infamous originated in Latin, but so did insufficient, and I can't find a concrete orgin of invaluable.
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6You should check the etymologies of those words: infamous is the opposite of famous, which used to simply mean "celebrated"; so the opposite is "not celebrated" (no positive aspect). Invaluable means the same thing as priceless: not that something has no value (or price) but that it is so valuable one cannot put a price on it (i.e., it cannot be "valued"). Etc. – Robusto Jan 18 '14 at 21:31
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3Because prefixes don't always mean the same thing. Just like whole words; bear is a verb meaning 'carry', and also a noun referring to an animal, and bare is an adjective meaning 'naked', and we never confuse them in speech. There are at least two in- prefixes. One is the negative one in insufficient. The other is the one in inside, and it means (surprise) *in*. That's the one in infamous, because it brings someone into fame (that's the etymology; you could look it up). As for invaluable, that's discussed here. – John Lawler Jan 18 '14 at 21:32
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1@John, where do you have that etymology for ‘infamous’ from? All Classical Latin senses of words related to infam- refer to ill fame, disrespect, dishonour, etc., clearly the privative prefix, rather than the preverbial preposition. This etymology is also given by etymonline and all other dictionaries I’ve been able to consult here. – Janus Bahs Jacquet Jan 18 '14 at 23:08
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Click on the in- link here. – John Lawler Jan 18 '14 at 23:32