Prove Corollary 0.3 using Theorem 0.2 please provide details thank you Let A be

Question

Prove Corollary 0.3 using Theorem 0.2

please provide details thank you

Let A be a set. Then, a number x is an upper bound of the set A if x ge y for all y A. A set A is bounded above if there exists an upper bound x of the set A. For this case, we say that A is bounded above by x. A number x is said to be the supremum (the least upper bound) of the set A if it satisfies the following two conditions: the number x is an upper bound of A, and if y is an upper bound of A. then x le y. For this case, we use the symbol sup A = x. Let A be a nonempty bounded above set. Then there exists the sup A. Let A be a nonempty set. Suppose that there exists the sup A. Then, for any delta > 0, there exists a number x [sup A - delta, sup A] A. Let f be a continuous function on [a, b]. Suppose f(a)

Explanation / Answer

Corollary 0.3 generalizes Theorem 0.2 by a simple shift of coordinates by the fixed number d. If f is a continuous function on [a,b] and f(a)

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