Learn English – What does “duly” mean in the phrase “duly noted”

'Wherein' is generally only used in formal writing. The Oxford English Dictionary gives the following senses and quotes. I have given the most recent quote, from which you can tell that the word is no longer generally used.

1. In what (thing, matter, respect, etc.)?

   1891 - Oh, Britannicus! wherein have we offended?

2. In which (place, material thing, writing, etc.)?

   1888 - Peering keenly into the shadow wherein she stood

3. In, at, during, or in the course of which (time).

   1819 - Length of days Wherein to act the deeds which are the stewards Of their revenue.

4. In which (matter, fact, action, condition, etc.); in respect of which.

   1889 - There began a round of pleasure for Julia wherein she was the central figure.

5. Into which.

   1585 - We came to an anker very nigh the castle, wherin when our patrone would followe vs [etc.].

To be nothing like means it is completely different and has nothing in common. Nothing like anything means incomparable; completely different from all other things. This is the literal meaning of the term, no figurative or idiom involved.

There are three examples of nothing like anything in the Corpus of Contemporary American English (COCA):

it was just an unbelievable event and nothing like anything the country had ever gone through before

Here the speaker means the event was completely unlike any event previously experienced in the country.

" It seems like I've always had some type of adversity, " Bobby says. " My freshman year at Duke, we lost the title game by 30 to UNLV.... But this is big adversity, nothing like anything else. # "

Here the speaker is referring to some type of adversity that this time has a magnitude never before seen, incomparable to any previous adversity.

" She spun around, drinking in the scenery, marveling at its almost palpable presence. " But... this is nothing like anything I've ever seen on the' net! "

Here, whatever it is the speaker is experiencing is unlike any experience she has had in the same environment.