1) I've never met a man as rich as him.
2) I've never met a man as rich as he.
3) I've never met a man as rich as he is.
Which one of the above-mentioned is correct (in formal scenario) and why? Also, how do I detect the subject and the object for this question?
What's happening in these sentences is that you are starting with an original idea like this:
I have never met a man who is as rich as he is rich.
That sentence sounds strange because we haven't applied any ellipsis- the process of pruning unnecessary or repeated items from a sentence. The minimum ellipsis for a natural sentence is to remove the repeated rich:
I've never met a man who is as rich as he is.
We can also remove the unnecessary who is (this is called whiz-deletion), giving your sentence 3:
- I've never met a man as rich as he is.
If you look at the original sentence, you will see the there are two instances of is, so we can also remove the duplicate is:
I've never met a man who is as rich as he.
Take out the who is and you get to sentence 2:
- I've never met a man as rich as he.
With all that ellipsis, many people will have lost touch with the grammar of the complete sentence, and feel uncomfortable with the he at the end of the sentence, so they change it to the first one:
- I've never met a man as rich as him.
This is what the majority of people would say in normal speech. When you look at writing (see this NGram), you will find significantly more sentences like 3, and a very small number of examples like sentence 2 - and mainly at the 'literary' end of the market. Meanwhile, sentence 1 hardly figures at all in written English: this gives a pretty good indication that sentence 1 is not generally considered acceptable in writing.
In a formal setting, 3 would be OK in any context and 2 would be acceptable in a literary context (poetry and novels, especially historical novels): 1 would be acceptable if it appeared in dialogue in a novel.
Jane is richer than him
As a conjunction, than requires a clause (which contains a subject pronoun):
Jane is richer than he is
For some reason, we prefer to treat than (and also the as ... as construction) as a preposition in everyday speech, but as a conjunction in formal writing. To quote in full the passage that Mari-Lou referred to in her answer:
Research associated with the Longman Grammar (1999) showed that speakers mostly use than (and as) as prepositions (i.e. with a following object pronoun) and only rarely with a following subject pronoun. Fiction writers make about equal use of the two constructions, while academic writers use neither.
All three are OK, some purists will argue that the second is formally correct
I've never met a man as rich as he
The use of the personal pronoun ‘he’ sounds more refined to some ears, more "British" and therefore more correct.
The majority of native speakers will use the object pronoun, and say
I've never met a man as rich as him.
Tagging the auxiliary verb at the end, is overkill in my opinion, but perfectly grammatical. Some might even call it redundant.
I've never met a man as rich as he is.
For a more technical explanation, Barrie England's answer (posted in 2011) includes this snippet from ‘The Cambridge Guide to English Usage’
[Emphasis in bold mine]
Research associated with the Longman Grammar (1999) showed that speakers mostly use than (and as) as prepositions (i.e. with a following object pronoun) and only rarely with a following subject pronoun.
Also related:
1. Is "she was younger than he" a grammatically correct expression?
2. "than her" versus "than she"
3. Is it wrong to say "You are smarter than me"?
4. "than I" vs. "than me"
In the most formal correspondence, e.g academic essays, contractions are best avoided, a higher-register term than rich should be used, and the auxiliary should accompany the subject pronoun.
I have never met a man as wealthy as he is.
For emphasis and greater effect, use inversion and brevity
Never have I met a wealthier man.
The "as ... as" construction is often used when you are comparing two people, things, or situations:
John is as rich as Jack.
An old woman with hair as white as snow.
Sometimes the second thing is not an explicit noun like:
Trump is as rich as he says.
In your case, the best formal one is the third sentence, "...is as rich as he is".
The second one, "...is as rich as he" is grammatically correct; this sentence implies the same as "... is as rich as he [is]" where the second "is" has been removed by ellipsis.
Most English speakers don't follow this rule, especially while speaking; they would say, "... is as rich as him."
First one is incorrect grammatically but used in common speaking. 2nd is less natural but I think correct. The best form in my opinion is 3rd. As, because, while, and since are a subordinating conjunctions, which require a subject pronoun.
Adding to the other answers, mainly to point out that this is not useless and actually can matter.
Consider the following two sentences:
1) I know you better than he.
2) I know you better than him.
The two sentences are both correct, but with different meanings. In their "complete forms", the sentences would look like this:
1) I know you better than he knows you.
2) I know you better than I know him.
All of these constructions sounds odd to my ear, the more natural construction, in my view, would be:
He was the richest man I ever met.
Of the three you offered, I would say "I never met a man as rich as he is" is the most correct but also the most stilted. "I never met a man as rich as he" sounds like deliberate emphasis for poetic effect (I would expect a subtle emphasis one the 'he' when spoken) whilst "I never met a man as rich as him" sounds most natural. Although, even then, I'd expect a native speaker to prefer a different construct such as the one I give above.
Saying it in slightly different words helps determine the correct pronoun:
I've never met anyone with as much money as he (has).
It would sound formal in conversation with many American speakers, who almost always (incorrectly) use the direct object pronoun (him) in these types of sentences.
