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Can someone please prove this for me?
Prove that the open unit interval (the set of all real x with 0 < x < 1) has cardinal number c. (Hint: map x --> x/(1+x), defined on all positive real numbers.)
The map suggested maps all the positive real numbers onto all the points in (0,1). The map is surjective (i.e it covers all points in (0,1)) and injective (two different points in R+ map into two different points in (0,1). Thus the cardinal of the interval is the same as the cardinal of R+ which is c (continuous).
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