I'm reading about sequences in Topology and I do not know how to solve this

let $\displaystyle R^1$ have the left ray topology

a) dose the sequence $\displaystyle f:N\longrightarrow R^1 $ given by $\displaystyle f(n)=\frac{1}{n} $ converges if so to what point or points

from definition f converges to $\displaystyle a\in R^1 $ if far all $\displaystyle U$ open in left ray topology and $\displaystyle a\in U$ there exist $\displaystyle n_o\in N$ such that if $\displaystyle n>n_o$ then $\displaystyle f(n)\in U$

ok if we take 1<= x in R and take U contains x take $\displaystyle n_o=1$ so any $\displaystyle n>n_o $ we have $\displaystyle f(n)\in U $

so f converges to all x>=1 is this right or not