Question

Let A be a non-empty set of rational numbers and B = {a+1 : a ∈ A} (sometimes denotes A + 1). Prove carefully that sup(B) = sup(A) + 1.

Answer 1

Answer:

a is an element of A; a is a rational number

(a+1) is element of B

Step-by-step explanation:

(a+1) = sup(A), which are the elements of B.

(a+1) + 1 = sup(B)

Recall a+1 = sup(A),

Therefore,

sup(A )+ 1 = sup(B)

sup(B) = sup(A) + 1 ___proved

Sup(A) means supremum of set A. It means least element of another set (say set B), that is greater than every element in set A