It is often argued that Trinitarian doctrine is contradictory. How can three be one and one be three, all at the same time? It sounds like bad math.
First, we need to recognize what is meant by the label "contradiction".
A logical contradiction is something that makes a claim and then also claims its exact negation. A logical contradiction cannot possibly be true. It is impossible for something to both be and not be at the same time and in the same way.
If I said "there is only one God and it is not the case that there is only one God", then I would be contradicting myself. If I said "there are three persons in the Godhead and it is not the case that there are three persons in the Godhead", then I would also be contradicting myself. However, I have not made either of those claims.
When I say that there is one family consisting of four persons, or one hand utilizing five fingers, or one race made up of multiple humans, I am not claiming anything contradictory. When I say that one chemical, such as H2O, exists in three states -- solid, liquid, and gas -- I am not being contradictory.
Likewise, saying that there is one God revealed in three persons that are eternally distinct is not contradictory. It may be difficult to grasp, and there may be no perfect analogy (certainly none of the analogies I used above fit the Godhead perfectly), but it is unquestionably not logically contradictory.
Not only is it not contradictory, but it is what God tells us about Himself in the scriptures.
In fact, Biblical Christianity is the only worldview that is not logically contradictory.