Constructive Mathematics

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3 domain-specific abstractions whose origin domain is Constructive Mathematics.

• Apartness relation — A constructive positive notion of distinction, typically irreflexive, symmetric and cotransitive, that is stronger than merely denying equality.
• Constructive nonstandard analysis — A constructive framework for infinitesimal and infinitely large reasoning that develops nonstandard analysis without classical choice-dependent foundations.
• Inhabited set — A set for which an element can be constructively exhibited or otherwise supplied as a witness, a stronger datum than double-negated nonemptiness in intuitionistic logic.