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The animation shows that numbers on the x-axis,  can be matched with  numbers on the interval -1<x<1 in such a away that:

1.  every x on the x-axis is matched with a different number in the interval -1<x<1,


2. all the numbers in -1<x<1 are used

hence, we can see that there must be the same number of numbers on the x-axis as there are on the interval -1<x<1. 

These numbers sets have the same Cardinality.

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