Chapter 9.5, Problem 46E

ch of these are partitions of the set of real numbers?

a) the negative real numbers, {o}, the positive real numbers

b) the set of irrational numbers, the set of rational numbers

c) the set of intervals $\left[k,k+1\right],k=\mathrm{...},-2,-1,0,1,2,\mathrm{...}$

d) the set of intervals $\left(k,k+1\right),k=\mathrm{...},-2,-1,0,1,2,\mathrm{...}$

e) the set of intervals

   $(k,k+1],k=\mathrm{...},-2,-1,0,1,2,\mathrm{...}$

f) the sets $\left\{x+n|n\in Z\right\}$for all $x\in \{0,1)$