Math and Arithmetic

Two lines with intersection is the empty set?


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2011-10-02 12:24:49
2011-10-02 12:24:49

It can be if the set consists of convex shapes, for example.


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The concept of closure: If A and B are sets the intersection of sets is a set. Then if the intersection of two sets is a set and that set could be empty but still a set. The same for union, a set A union set Null is a set by closure,and is the set A.

Easily. Indeed, it might be empty. Consider the set of positive odd numbers, and the set of positive even numbers. Both are countably infinite, but their intersection is the empty set. For a non-empty intersection, consider the set of positive odd numbers, and 2, and the set of positive even numbers. Both are still countably infinite, but their intersection is {2}.

Not necessarily. The odd integers and the even integers are two infinitely large sets. But their intersection is the null (empty) set.

In Euclidea space it is either a point or the two lines - which must be coincident. ----- Intersection = the point/s where the two lines meet in space. It is a point or set of points that are common to two or more geometric configurations (also called "product" - the set of elements that are common to two sets).

Because they are disjoint, (ie. they contain none of the same elements) their intersection (what they both share in common) is the empty or null set.

An intersection is the region of space that forms when two forms overlap (the intersection of two lines makes a point, the intersection of two planes makes a line, etc.). In set theory, it is the set formed when two or more sets overlap in terms of common elements. With respect to roads, it is the place where two roads cross each other.

They can be two arcs, like the outline of a crescent moon, or a contact lens. Two straight lines on a plane surface cannot have two points of intersection: there can only be 0, 1 or infinitely many.

I presume you mean intersecting. Two sets are intersecting if they have members in common. The set of members common to two (or more) sets is called the intersection of those sets. If two sets have no members in common, their intersection is the empty set. In this case the sets are called disjoint.

You normally do not have an intersection of only one set. The intersection of a set with itself is the set itself - a statement that adds little value. The intersection of two sets is the set which contains elements that are in each of the two sets.

If B = {10111213} and C = {1213} then their intersection is the empty set, {}.The union of A with an empty set is set A.

Given two or more sets there is a set which is their union and a set which is there intersection. But, there is no such thing as a "union intersection set", as required for the answer to the question.

No, only if both sets are empty. The intersection of disjoint sets is always empty.

In general no. The intersection of two parallel half-planes A and B is either a half-plane (either A or B, when A and B have similar orientation) or the empty set (when A and B have opposite orientation). When A and B are not parallel, their intersection is a maximal open region bounded by the two lines that define A and B, respectively. In this case, the intersection always exists and it is never a half-plane.

A set of parallel lines will have no intersection. But they may intersect other lines.

Yes. You can obviously have a set of lines with no common intersection, can't you?

The intersection between rational and irrational numbers is the empty set (Ø) since no rational number (x∈ℚ) is also an irrational number (x∉ℚ)

Two sets are said to be "disjoint" if they have no common element - their intersection is the empty set. As far as I know, "joint" is NOT used in the sense of the opposite of disjoint, i.e., "not disjoint".

The intersection of two or more solids can either be an empty set, a point (two cones "intersecting" apex-to-apex), a line (two cubes touching along one edge), a face (two cubes, face-to-face). If the solids are "filled", the overlapping intersection will be another solid. If they are hollow, it will be a closed three dimensional figure.

The intersection is the set of solutions that satisfy two or more mathematical expressions.

ExplanationFormally, two sets A and B are disjoint if their intersection is the empty set, i.e. if This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint andSets that are not the same.

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.)

the other one is intersection

No. It can be infinite, finite or null. The set of odd integers is infinite, the set of even integers is infinite. Their intersection is void, or the null set.

It means meet. Point of intersection is the point where shapes or lines meet. With regard to sets, the intersection of two sets is the set of elements that are common to both sets. For example, the intersection of the set of the first five whole numbers and the set of the first five odd numbers is the set of the first three odd numbers. This is expressed as {1, 2, 3, 4, 5} ∩ {1, 3, 5, 7, 9} = {1, 3, 5}

An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.

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