In: Advanced Math
Mathematics real analysis(please follow the comment)
Theorem: There exists a unique positive real number a is in R, satisfying a^2=2
Please proof it. Hint(you need to prove Uniqueness and Existence. For Existence(you need to let a=supA and prove contradicts a^2<2, a^2>2 also use the Archimedean property) Show every steps. Use contradiction proof