|Jul15-12, 07:08 PM||#1|
Rudin Theorem 1.20 (b)
I understand the proof except for the following:
Suppose that -m2 < nx < m1 for positive integers m1, m2, n, and real number x.
Then there is an integer m with -m2 ≤ m ≤ m1 such that m-1 ≤ nx < m.
It definitely sounds reasonable, but it seems like a big jump in logic.
|Jul15-12, 07:26 PM||#2|
Let m be the least integer that is strictly greater than nx. It is a triviality to verify that this integer has the desired properties.
|Mar23-13, 12:25 PM||#3|
I have attached a simple demonstration of the bit you are asking.
Let me know if it is clear now.
I hope it helps
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