Great great great

大した is actually two words. 大, meaning big, and した is the past tense form of する, to do.

So 大した is really “to make something big” which can be translated as “something good” or “great”.

大きさ and 大きい relate to size and the other posts about さ denoting the noun form of an adjective are pretty spot on:

大いに is two things as well:

  1. The adjective 大い, meaning “a great deal” or “very much”
  2. The target particle に

So, the meaning of “very” is because it’s used to describe when there is a great deal of something.

Now, you can just memorize them as is and get it to stick, but I find that breaking them down helps me to keep them straight in my head.

Hope this helps.

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