I have the blood of both an English teacher and a former algebra teacher coursing through my veins. A blessing in many ways, but as such, I have a strong tendency to dissect the English language with an overwhelmingly logical mind, often to the annoyance of people within a 10-foot radius. (And you.)
But bear with me, because I've found something that will make your head explode.
Commonly, the "in-" or "un-" prefix negates the meaning of a word. For instance, "flexible" vs "inflexible", or "tie" vs "untie". This is the case the vast majority of the time...but not always, for no good reason at all, such as with "flammable" vs "inflammable", which essentially mean the exact same thing. (Look it up.)
My co-workers and I ran across another interesting example the other day.
Consider "valuable", which describes something that has tangible value. A Babe Ruth rookie card has value. Now consider "invaluable", which frequently is used as a more intense version of "valuable". Friendship, for one, is invaluable. Literally, if an object is invaluable, then it has no value; not because it isn't precious, but because the object is so valuable that its value cannot be quantified...if that makes sense. "Invaluable", therefore, has a very positive connotation.
Now consider "worth". The aforementioned Babe Ruth rookie card has lots of worth, in the same way that it has lots of value. But friendship is so precious that its worth cannot be measured. So would you describe friendship as "worthless"? Even though this is exactly the same line of reasoning we followed from "valuable" to "invaluable", the word "worthless" has a strong negative connotation. Friendship isn't worthless, but that lousy novelty t-shirt you got from your distant relative for Christmas might be.
How is this possible? "Value" and "worth" are synonyms. But negating them as shown above, getting "invaluable" and "worthless", are antonyms.
No doubt this is because the words evolved in different ways through the years. Sort of like "terrific" came to mean something very positive, even though it springs from same root as the word "terror", which ain't so positive.
Just another way the English language don't make no sense.
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