The Italian word infatti is a useful conjunction whose purpose is to confirm, prove or justify a previous statement, much like the English terms in fact, as a matter of fact and indeed.
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Here is an example that shows how infatti can be used in a sentence.
Non mi piace il caffè: infatti non lo bevo mai.
I don’t like coffee: in fact I never drink it.
You can also use infatti in an ironic sense, in which case it is often translated as but of course.
Ha promesso di aiutarmi a traslocare, e infatti non si è fatto vivo!
He promised to help me move but of course he didn’t show up!
In this sense, you may also see it used alone, with the rest of the sentence being implied.
Ha promesso di aiutarmi a traslocare, e infatti…!
He promised to help me move but…!
As an adverb and on its own, infatti can function as a response to a statement to express agreement. In English, we might use exclamations such as Exactly! Indeed! That’s right! Tell me about it! or Yeah, I know!
Dovevano passare a prenderci alle sette… – Infatti! Ma dove cavolo sono?
They were supposed to pick us up at seven… – Exactly! Where on earth are they?
Mi sono veramente divertito l’altra sera! – Infatti! Dobbiamo uscire più sovente!
I had so much fun the other night! – Yeah, I know! We have to go out more often!
A synonym of infatti is difatti. Other similar words include in realtà, invero and in effetti.