## Question

###### Suppose Xis nonempty subset of R that is bonded above: Let Y = {Zx:x â‚¬ X} Let & supX. (1) If a is an upper bound ofX, show Za is an upper bound of Y: (Hence, this shows that Za is an upper bound of Y.) (2) Use the definition of the least upper bound to prove that Za supY .

Suppose Xis nonempty subset of R that is bonded above: Let Y = {Zx:x â‚¬ X} Let & supX. (1) If a is an upper bound ofX, show Za is an upper bound of Y: (Hence, this shows that Za is an upper bound of Y.) (2) Use the definition of the least upper bound to prove that Za supY .

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