  Given a uniformly convergent sequence of ambient isotopies
$(H_n)_{n\in\mathbb{N}}$, bijectivity of the limit function $H_\infty$ together
with a minor compactness condition guarantees that $H_\infty$ is also an
ambient isotopy. By offloading the uniform convergence hypothesis to a more
diagrammatic condition, we obtain sufficient conditions for performing
countably-many Reidemeister moves. We use this to construct examples of tame
knots with countably-many crossings and discuss what distinguishes these from
similar-looking wild curves.
