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*[[Constructivist analysis]], which is built upon a foundation of [[constructivist logic|constructivist]], rather than classical, logic and set theory.
*[[Intuitionistic analysis]], which is developed from constructivist logic like constructivist analysis but also incorporates [[choice sequence]]s.
*[[Non-Newtonian calculus]], which provides alternatives to the classical calculus of Newton and Leibniz.
*[[Non-standard analysis]], develops rigorous infinitesmals within a new number system along with a transfer principle allowing them to be applied back to the real numbers.
*[[p-adic analysis]]
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