Cartesian Products

   

                                                  Cartesian Products

                                                        September 11

                                                By Watheq Al-Bnosha

Introduction:

Cartesian Product is the combination of all ordered pairs of two series, such that each element of the first series  goes with all of the elements of the second series. For example, if we have two series $A$ and $B$. $A$ contains (1,3,5), and $B$ contains (2,4), so $A\times B$= {($A\times B$)| $A$∈$A$ and $Y$∈$Y$}

As shown in Fig.1

Fig. 1

Topologically, we can get many shapes when applying Cartesian products. For example, we get a torus when we multiply two circles which means that every point in the first circle is multiplied by every single point of the second circle to form the torus. $S^1\times S^1$

As it it shown in Fig.2

Fig. 2

And we get a cylinder by multiplying $I$\times $S^1$

^{where $I$ is just a straight line that goes from 0_________1}

Fig.3