Imply or infer?

We imply something by what we say. We infer something from what somebody else says. The main difference between these two words is that a speaker can imply, but a listener can only infer.

When someone implies something, they put the suggestion into the message:

Are you implying that the team cheated?

When someone infers something, they take the suggestion out of the message. In order to underline this difference, infer is used with the preposition from:

Then I think we must infer from what they said that they believe we should reapply for the job.