billswift comments on Counterfactual resiliency test for non-causal models - Less Wrong
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At least for the three examples you cited, I seem to remember them bring called approximations, not "correct".
What's the difference between a singularity, and an approximate singularity? :-)
In the former case, it progresses asymptotically, while in the latter, it progresses exponentially or super-exponentially but not asymptotically.