Using your knowledge, show that the set [0;1) (the non-negative real numbers) does not satisfy the Well-ordering principle. In other words, show that it contains a

subset A which does not contain the smallest element.

Theorem 7.12 (Wellerdering Principle). Every nanempty set A C N has its smattsst element, that ts an an. E A such that ac. E a for all a E A. In other words, ever},r nenempty set of natural numbers has the smallest element. Note that many ether sets1 eg. the interval (0, 1), do not have the smallest element