Ordering of Squares in Reals
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Theorem
Square of Real Number is Non-Negative
Let $x \in \R$.
Then:
- $0 \le x^2$
Real Number between Zero and One is Greater than Square
Let $x \in \R$.
Let $0 < x < 1$.
Then:
- $0 < x^2 < x$
Real Number Greater than One is Less than Square
Let $x \in \R$.
Let $x > 1$.
Then:
- $x^2 > x$