Prove Proposition. In other words, show that if az is a real number and n an...

Transcribed Image Text:

Prove Proposition. In other words, show that if az is a real number and n an integer, then (a) [x]<n if and only if a <n, (b) n< [a] if and only if n < x, (c) n< [a] if and only if n < x, (d) [a]<n if and only if a <n. As a cautionary tale, find counterexamples to each of the following state- ments: (e) [x] <n if and only if a <n, (f) n< [a] if and only if n < x, (g) n< [a] if and only if n ≤ a, (h) [a]<n if and only if a <n. The moral of the story is that you need to be very careful when you omit floor or ceiling functions in integer comparisons. Prove Proposition. In other words, show that if az is a real number and n an integer, then (a) [x]<n if and only if a <n, (b) n< [a] if and only if n < x, (c) n< [a] if and only if n < x, (d) [a]<n if and only if a <n. As a cautionary tale, find counterexamples to each of the following state- ments: (e) [x] <n if and only if a <n, (f) n< [a] if and only if n < x, (g) n< [a] if and only if n ≤ a, (h) [a]<n if and only if a <n. The moral of the story is that you need to be very careful when you omit floor or ceiling functions in integer comparisons.

Answer rating: 100% (QA)

a lfloor x rfloor n if and only if x n if If lfloor x rflo... View the full answer