Excercise 5.4.3 only Prove the remaining claims in Proposition 5.4.7. Exercise 5

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Excercise 5.4.3 only

Prove the remaining claims in Proposition 5.4.7. Exercise 5.4.3. Show that for every real number x there is exactly one N such that N x N + 1. (This integer N is called the integer part of x, and is sometimes denoted N = [x].) Exercise 5.4.4. Show that for any positive real number x > 0 there exists a positive integer N such that x > 1/N > 0. Exercise 5.4.5. Prove Proposition 5.4.14. Exercise 5.4.6. Let x, y be real numbers and let > 0 be a positive real. Show that |x - y| 0 if and only if x y. Show that |x - y| for all real numbers > 0 if and only if x = y.

Explanation / Answer

here we take two integers n and m

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