**Examples**

**Z**in**R**has no upper bound.- Let the relation "≤" on {
*a*,*b*,*c*,*d*} be given by*a*≤*c*,*a*≤*d*,*b*≤*c*,*b*≤*d*. The set {*a*,*b*} has upper bounds*c*and*d*, but no least upper bound. - In
**Q**, the set of numbers with their square less than 2 has upper bounds but no least upper bound. - In
**R**, the set of numbers less than 1 has a least upper bound, but no greatest element. - In
**R**, the set of numbers less than or equal to 1 has a greatest element. - In
**R**² with the product order, the set of (*x*,*y*) with 0 <*x*< 1 has no upper bound. - In
**R**² with the lexicographical order, this set has upper bounds, e.g. (1, 0). It has no least upper bound.

Read more about this topic: Greatest Element

### Famous quotes containing the word examples:

“Histories are more full of *examples* of the fidelity of dogs than of friends.”

—Alexander Pope (1688–1744)

“There are many *examples* of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”

—Bernard Mandeville (1670–1733)

“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied *examples* of his wrath.”

—G.C. (Georg Christoph)

Related Subjects

Related Phrases

Related Words