(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let a,b [tex]\in[/tex]R with a < b. and let n [tex]\in[/tex]N where n(b-a) > 1.

a) How do you know that such an n must exist?

b) Show that there exists m [tex]\in[/tex]Z where a < m/n < b

c) Show that there exists some irrational c where a < c < b (Hint:rational + irrational = irrational.)

2. Relevant equations

see above btw N is for natural numbers, Z for integers and R for real numbers

3. The attempt at a solution

a) Since n(b-a) > 1 , n > 1/(b-a) and since b does not equal a there is an n which exists OR can we say that nb > na and the n's cancel out to give us the condition given in the question.

b) we already know that n is natural and N[tex]\subset[/tex]Q and its safe to assume that Z[tex]\subset[/tex]R is always true but how do I exactly show that m lies in Z.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Natural numbers, integars

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