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Gerardo Toraldo » 5.Continuity

Law of continuity

Law of continuity (Math. & Physics), the principle that nothing passes from one state to another without passing through all the intermediate states.

Leibnitz was the first to apply it extensively in the test of physical theories, and in the reduction of fragmentary knowledge to order and intelligibility.
He affirmed that nothing passes from one state to another without passing through all intermediate states, and established the truth of his proposition by showing the absurdity of the contrary. If a change were to happen without the lapse of time, the thing changed must be in two different conditions at the same instant, which is manifestly impossible
(George Iles).

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  • Theorems about functions continuous on intervals
  • Application to the determination of the range of a function
  • Application to the approximate solution of f(x)=0
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