In 10-14 s denotes the sets of real numbers strictly between 0 and 1. That is
Let . Prove that S and V have the same cardinakity.
The sets have the same cardinality, where and
Let be the set of all real numbers that are between .
A function is said to be one-to-one function if the distinct elements in domain must be mapped with distinct elements in co-domain.
A function is onto function if each element in co-domain is mapped with atleast one element in domain.
Let be the set of all real numbers which lies between .
That is .
Let be the set defined as .
The objective is to show that have same cardinality.
Define the function , for all .
To show: is one-to-one.
Let such that
Therefore, is one-to-one
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