Prove Theorem 11.2.1(b): If f and g are real-valued functions defined on the same set of nonnegative integers and if and for every integer , where r is a positive real number, then if is if, and only if is and is .
The proof of the given statement.
The given statement is,
“Two real valued functions and are defined on the same set of non-negative integers and if and for every integer , where is a positive real number, then is if and only if is and is ”.
, then according to the definition of ,
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