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Mathematical objects intersect when they have something in common. For example, the sets {1,2,3,4} and {2,4,6} intersect as {2,4}.

For two sets A and B, their intersection is written as A∩B and is formally defined as A∩B = {x|xϵA AND xϵB}.

From geometry we have another example. Euclid postulated that:

When two lines are not parallel, they must intersect.

Non-Euclidean geometry concerns geometries where the conclusion need not hold.