I found that inequalities can be embedded in Calculus to form their unique theorems such as its integration, differentiation, Mean-Value Theorem, Taylor Expansion, Riemann partition. And discrete statistics, continuous statistics and norms can also embedded. Average type inequalities, integration operators, differential operators, Riemann partitions , discrete statistics, continuous statistics ,and norms will have one-one onto correspondence. And it can have higher dimension extension. The first part states the embedding which forms Calculus space, the second part states the first part can naturally induce extension of addition, subtraction, multiplication, and division. And the third part states a method which can handle probability distribution fitting.