Many a man died in that battle.
My understanding of many mean more than 2 and a man mean 1. But in the sentence above, these two words are put together and I wonder what does it really mean? How can you have many one man died in that battle?
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This is what Merriam-Webster's Learner's Dictionary has to say about this (maybe a bit too lengthy), on its Ask the Editor subpage:
The word many has two common functions:
A) It is often used as an adjective that describes a plural noun and tells us that there is a large number of that noun, as in these examples:
1. She worked hard for many years. 2. They were one of the many, many families that came to watch the parade._
B) Many is also commonly used as a pronoun, to mean “many people or things,” as in these examples:
1. Some people will come to the meeting, but many [=many people] will not.
2. We were hoping to sell our old books, but many [=many books] were not in good condition._
3. I know some of the people here, but not very many.
The fixed expression many a/an... is more formal than the single word many, and it is much less common. Many a/an... is used mainly in literary writing and newspapers. Like the adjective and pronoun many discussed above, many a/an... is used to indicate a large number of something. However, it takes a singular noun, which can be followed by a singular verb. Here are some examples:
1. It remained a mystery for many a year. [=for many years]
2. I've been there many a time. [=many times]
3. Many a politician has promised to make changes. [Politician and has are singular.]
And here's Oxford Advanced Learner's Dictionary, saying:
many a (formal): used with a singular noun and verb to mean ‘a large number of’:
Many a good man has been destroyed by drink.
So, they practically mean the same thing, but the second one is more formal, and less common in modern English.
It doesn't say "many one man."
Normally, we would say "Many men died in battle." It's a simple factual statement.
"Many a man died in battle" has a similar meaning; it's just a different way of saying it. I'm not sure if there's a term for this kind of speech, but it sounds more literary, dramatic or poetic (to me, at least).
Merriam-Webster's analysis is lacking one very important aspect of this use, in that "many a man" is just a tried and true method (or literary device) employed to add emphasis. The disagreement between the plural "many" and the singular "man" serve to grab the reader or listener's attention, and in this particular example, to individualize what is a collective tragedy. The horror of watching man after man (many a man) die in battle.
IMO Merriam-Webster could do more to explain why such phrasing is used by writers and journalist.