Order RelationsAssume that the real line has the least upper bound property.(a) Show that...

Order Relations

Assume that the real line has the least upper bound property.

(a) Show that the sets

have the least upper bound property.

(b) Does [0, 1] × [0, 1] in the dictionary order have the least upper bound property? What about [0, 1] × [0, 1]? What about [0, 1] × [0, 1]?