1) Uniqueness property
The suprumum and infimum of a bounded subset S of Ɍ, if exist is unique.
2) Approximation Property
Let A be a non- empty set in Ɍ which is bounded abouve and b = sup A. Then for any c ˂ b there exist x in A such that c ˂x≤ b.
3) Additive property
Let two non - empty sets A & B are given. Let C = { x+ y: x ɛ A and y ɛ B} . If each of A & B has supremum then C has also supremum and SupA + supB = supC.
4) Comparison property
Let A & B be two sets in Ɍ such that x ≤ y for all x belongs to A and for all y belongs to B. If B has supremum hence SupA ≤ supB.
The suprumum and infimum of a bounded subset S of Ɍ, if exist is unique.
2) Approximation Property
Let A be a non- empty set in Ɍ which is bounded abouve and b = sup A. Then for any c ˂ b there exist x in A such that c ˂x≤ b.
3) Additive property
Let two non - empty sets A & B are given. Let C = { x+ y: x ɛ A and y ɛ B} . If each of A & B has supremum then C has also supremum and SupA + supB = supC.
4) Comparison property
Let A & B be two sets in Ɍ such that x ≤ y for all x belongs to A and for all y belongs to B. If B has supremum hence SupA ≤ supB.
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