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I would like know whether it is somehow possible to analytically get discontinuities of a given function on a given interval (possibly with some reasonable assumption of the function otherwise being well-behaved)

To give an example I would like a function Discontinuities that behaves something like this:

( *In *) Discontinuities[Sign[x], {x,-1,1}]
(* Out *) {0}

(* In ) Discontinuities[Floor[2x], {x,-1,1}]
( Out *) {-1/2,0,1/2}


(* In ) Discontinuities[CDF[BinomialDistribution[2, 1/2], x], {x, -1, 3}]
( Out *) {0,1,2}
user1747134
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    This is a slightly related discussion – Artes Aug 19 '20 at 11:55
  • Interesting. Something similar could work using the analytical definition of discontinuity. How could I make a subexpression like Limit[Sign[x], x -> 0, Direction -> "FromAbove"] not directly evaluate, so I can Reduce it for x in a logical formula requiring limit "FromAbove" and "FromBelow" to be different at point x? – user1747134 Aug 19 '20 at 12:32
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    There's one in the Wolfram Function Repository here. – Greg Hurst Aug 19 '20 at 13:20
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    Specifying the interval in the form {x, -1, 1} is ambiguous as to whether the endpoints should be included. Including intervals as constraints (e.g., {f[x], -1 < x < 1} or {f[x], -1 <= x <= 1}as used in "FunctionDiscontinuities") eliminates the ambiguity. – Bob Hanlon Aug 19 '20 at 15:55

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