It's not that she believes it. It's that she dares to contradict the state. 2+2=5.
In 1984, "2+2=5" is a false statement created by the Party and an example of the many ways the Party controls people. In making people believe that a random, false statement is an objective truth, the Party distorts and claims control of truth itself. Winston understands that slogans like "2+2=5" are mechanisms of the Party's social control.
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