Is Than I correct of Than me?

than /ðæn; (unstressed) ðən/
conj , prep (coordinating)
1.used to introduce the second element of a comparison, the first element of which expresses difference: shorter than you, couldn't do otherwise than love him, he swims faster than I run
2.used after adverbs such as rather or sooner to introduce a rejected alternative in an expression of preference: rather than be imprisoned, I shall die

Etymology: Old English thanne; related to Old Saxon, Old High German thanna; see then
USAGE
In formal English, than is usually regarded as a conjunction governing an unexpressed verb: he does it far better than I (do). The case of any pronoun therefore depends on whether it is the subject or object of the unexpressed verb: she likes him more than I (like him); she likes him more than (she likes) me. However in ordinary speech and writing than is usually treated as a preposition and is followed by the object form of a pronoun: my brother is younger than me