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With only 140 characters to use in each tweet, it isn't enough to sustain a full conversation over a short or long period of time. By the time you get past the introduction or the simple 'hello', you find that you've already churned up more characters than you have access to.
Though Facebook has a character limit in each status, it's easy to tag people in - like Twitter. But Twitter is incredibly public, whereas Facebook can at least be limited to a smaller group of friends using extensive set of privacy controls.