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No. Say for example interval A is (-inf, 0), and interval B is (0, inf). Even though they are both infinite, their intersection is the empty set (i.e. they have nothing in common). The same applies to sets. That being said, it is entirely possible for two infinite intervals' intersection to be infinite. All that is required is that one is a subset of the other (one set contains all of the other set, for example A = (0, inf) and B = (1, inf). Here, A contains all of B, and therefore, their intersection is B. This means that their intersection is infinite.)
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Can a line be formed by the intersection of two planes?
ONLY a line can be formed by the intersection of two planes...and always.
Is a line is defined to be the intersection of two planes?
A line is infinite but a line segment has end points and a midpoint
Do the intersection of two sets always contains a smaller number of terms than the union of two sets?
No, because the intersection of two equivalent sets will have a union the same size as its intersection.
Is The intersection of two nonempty sets is always nonempty?
Not necessarily. The odd integers and the even integers are two infinitely large sets. But their intersection is the null (empty) set.
Two planes always intersect in what geometric figure?
The intersection of two planes is one straight line.
