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.

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