# Math Help - Monotonically Increasing

1. ## Monotonically Increasing

For each n $\in$ N let $f_{n}$ : [a,b] $\rightarrow$ R where a,b $\in$ R are such that a < b. Show that if F : [a,b] $\rightarrow$ R is such that $F_{n} \rightarrow$ F as n $\rightarrow \infty$ in a pointwise fashion for each n $\in$ N the function $F_{n}$ is monotonically increasing, then F is monotonically increasing.

2. Take x<y, you know that $F_n(x)\leq F_n(y)$. What happens when you tend to the limit as n goes to infinity?