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Are there really sufficiently many assignable pixel locations such that you can drag a Controller to such a resolution? Would you be satisfied if the range were small enough that the MinIntervalSize you seek could be rendered? After all, this will work: IntervalSlider[{.003, .007}, {0., .010}, ImageSize -> 600, MinIntervalSize -> .00000001, ...


I reported the issue discussed in this question to Wolfram technical support. I have received the following reply: It does appear that Animator is not behaving properly in this case and I have forwarded an incident report to our developers with the information you provided. On the basis of this reply, I have tagged this question with bugs.

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