I am reading the book Reinforcement Learning: An Introduction. Second edition (Richard S. Sutton and Andrew G. Barto). In the k-armed bandit problem using $\varepsilon$-greedy selection method, the authors say that
An advantage of these methods is that, in the limit as the number of steps increases, every action will be sampled an infinite number of times, thus ensuring that all the $Q_t(a)$ converge to their respective $q_*(a)$.
May I ask why "every action will be sampled an infinite number of times" since at each time step $t$ (for limited time steps), we only select one action $A_t = a$?