认为 vs 以为

认为 states a considered opinion (我认为你知道那不是真的); 以为 voices a supposition — usually a mistaken one (你真的以为我会帮你吗？).

认为認為

rènwéi ㄖㄣˋ ㄨㄟˊ

to believe; to think; to consider; to feel

我们认为他们不会买新车。

We do not anticipate their buying a new car.

以为以為

yǐwéi ㄧˇ ㄨㄟˊ

to think; to believe (often with the implication that the belief is mistaken – unless referring to one's own current belief)

以前的人以为地球是平的。

It used to be thought that the earth was flat.

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