# Relationship between rate of convergence and order of convergence

What is the difference between rate of convergence and order of convergence? Have they any relationship to each other? For example could i have two sequences with the same rates of convergence but different orders of convergence, and vice versa?

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The order of convergence doesn't tell you everything. A numerical integration scheme with step size $h$ could have cubic order of convergence, so the errors go as $O(h^3)$, but the true error could be $100000h^3 + \ldots$, which would mean that for many practical problems the rate of convergence is actually quite slow.