Out of context, they could all be correct. The choice between using "the" or omitting it depends on the context in which you say these sentences. In general, "the" is possible when you're comparing a person or thing with another person or thing.
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IvanhrIf, on the other hand, you're comparing the same person or thing in different situations, "the" isn't possible.If that's true, (4) is wrong, isn't it? Because we're talking about the same person in (3)/(4).
JungKimIf that's true, (4) is wrong, isn't it? Because we're talking about the same person in (3)/(4).Yes, if you're referring to the one occasion when she ran fastest (and didn't compete with other people). This distinction is not usually observed in everyday speech, possibly because people are not really aware of it.
enoonNumber three is not English. The rest are fine.OK. How about 5) and 6) then?
JungKimHow about 5) and 6) then?5) She ran fastest in the world.6) She ran the fastest in the world.Neither one is English.
enoon JungKimHow about 5) and 6) then?5) She ran fastest in the world.6) She ran the fastest in the world.Neither one is English.Come on, enoon. Yes, it's much better (and more more natural) to say "She's the fastest runner in the world" but to say they're not English is just plain wrong.
Ivanhr enoon JungKimHow about 5) and 6) then?5) She ran fastest in the world.6) She ran the fastest in the world.Neither one is English.Come on, enoon. Yes, it's much better (and more more natural) to say "She's the fastest runner in the world" but to say they're not English is just plain wrong.They are blatantly unidiomatic. Neither one is a possible natural