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Oliga [24]
3 years ago
8

Sketch the Cartesian product on the x-y plane R^2: Zx Z.

Mathematics
1 answer:
Minchanka [31]3 years ago
7 0

Answer:

\mathbb{Z}\times \mathbb{Z}=\{(a,b)\lvert a, b\in \mathbb{Z}\}

Step-by-step explanation:

In general, the Cartesian product of two sets A,B is a new set defined by

A\times B=\{(a,b)\lvert a\in A,b\in B\}

The pair (a,b) is ordered pair because the order is important, that is to say, in general (a,b)\neq (b,a).

One of the most important Cartesian products in mathematics is \mathbb{R}\times \mathbb{R}=\{(x,y) \lvert x,y \in \mathbb{R}\} which is precisely the Cartesian Plane xy. The set \mathbb{Z}\times \mathbb{Z} is a subset of \mathbb{R}\times \mathbb{R} which is the set of all the points in the Cartesian plane whose coordinates are integers numbers. So, sketching the set \mathbb{Z}\times \mathbb{Z} we have a picture as the shown below.

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