Intersection is a junction where one street or road crosses another. Synonyms include crossroad, crossway, crossing, carrefour.

Intersections usually come with traffic lights and street signs which specify rules of passage. Although, they don't have to have any of those when two equal, minor streets intersect, because in that case the vehicle at one's right hand side will have the right of way. The lights will also be unnecessary on many of the intersections where one of the roads is minor compared to the other one.

Another thing that most intersections have are zebra crossings or crosswalks, which are used by pedestrians to cross the road without danger of being run over by a moving vehicle. Zebra crossings aren't necessary when there aren't any walkways near the road.

There are also traffic islands, small usually elevated patches of land for the traffic lights and walkways, but they exist only on intersections large enough to actually need them.

A very simple intersection looks like a cross:

```   | |
---' '---
---. .---
| |
```

An intersection of two-way streets looks like this:

```   | | |
---' | '---
-----+-----
---. | .---
| | |
```

An intersection of two-way streets with traffic lights and crosswalks looks like this:

```    | | |
|||||
--==o | o==--
--==--+--==--
--==o | o==--
|||||
| | |
```

A little more complicated intersection, of larger roads, looks like this:

```    | | | | |
|||||||||
--==o--o. . o==--
--==........|==--
--==o.......o==--
--==|........==--
--==o . .o--o==--
|||||||||
| | | | |
```

The line towards the middle of each of the roads isn't meant to represent a swastika, rather a horizontal pipe some four meters over the ground with another traffic light. There's only so much I can do in ASCII.

Note also that this is how it looks like in countries where you drive on the right side of the road; in countries that drive on the left most of these things are analogous but inversed.

Crossroad intersections are said to be less efficient than roundabouts, yet much more popular (because of tradition and usually smaller size, I suppose).

can you believe nobody has noded this particular meaning yet?

# Set Theory

Set theory defines an intersection operation. For any nonempty set A, the set

B=A = { x : y.y∈A⇒x∈y }.
B is the set of "all elements of all elements" of A: those elements that are in each member of A.

No axiom is required to guarantee the existence of A: A is non-empty, so there is some a∈A. And A can be generated as a subset of a. Define the predicate P(x) = ∀y.y∈A⇒x∈y, and then define

A = { x∈a : P(x) }
In essence (and unlike the case for the union A), the cardinality of A is (easily) bounded, so no new axiom is required to generate it.

When A={a,b} is a pair (derived e.g. by the axiom of pairing), we use the more common notation a∩b = A. This notation is also used when a=b.

When A is an indexed set A = {ai: i∈I} for some index set I, notations based on ∩i∈Iai = A are common. Thus, we may see

= n=1 {k∈N : k≥n}.

These less formal notations are more common in most of mathematics.

Given a "universal" set in which to take complements, intersections are related to unions by means of DeMorgan's laws. But as we've seen, in the general case (when there is no a priori universal set), intersections are much simpler than unions: They require no axioms. They also give less, as they only ever decrease cardinality.

In`ter*sec"tion (?), n. [L. intersectio: cf. F. intersection.]

1.

The act, state, or place of intersecting.

2. Geom.

The point or line in which one line or surface cuts another.

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