Let A is the system of semi$-$open segments $\{[0,$ n$)$; n is a integer$\}$ in R$.$

i$)$ Is A a $\backslash$sigma $-$field?

ii$)$ Describe the $\backslash$sigma $-$field F generated by A$.$

iii$)$ Which functions from R to R are F$-$measurable?

iv$)$ Establish that the set of measurable functions has the power of continuum