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The importance of a good education cannot be overestimated. [=a good education is very important]

http://www.learnersdictionary.com/definition/overestimate

I'm confused of this explanation in parentheses.

I think if I rewrite the first sentence like "The importance of a good education cannot be underestimated", then this may fit in the explanation "a good education is very important." Am I right?

  • As discussed in "What do native speakers think of word roots?", your vocabulary is the collection of words that you can use and/or understand. Each word in your vocabulary is a distinct vocabulary word; it is not a distinct vocabulary. – Jasper Apr 10 '16 at 12:11
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  1. The importance of a good education can not be overestimated.

A good education is so important that it is impossible to consider it more important than it actually is, because it is of utmost or paramount importance

  1. The importance of a good education must not be underestimated.

A good education is so important that we must never consider it of little importance or marginal. Although it might not be the most important thing, we should take care to assign it its true importance.

  • Native speakers often get these kinds of statements bolixed up. – Tᴚoɯɐuo Apr 11 '16 at 15:34
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No. You are wrong. What your second sentence means is that no estimation of the importance is lower than the actual importance. That means that the actual importance is lower than anything else. It's very unimportant.

When you use the first sentence, it means that no estimation is higher than the actual importance. If nothing is higher, that means it must be the highest. Therefore, it is very important.

Your sentence is similar to the often-used "I could care less". It means that how much you care is not the lowest that could be cared. What people mean to say is "I couldn't care less".

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