An infinitesimal is a quantity approaching zero but not zero, crucial in non-standard analysis. It allows for rigorous calculus using…
The inductive step of a proof by induction demonstrates that if a property holds for any arbitrary element 'n', it…
An independence result demonstrates that a statement is neither provable nor disprovable within a specific axiomatic system, assuming the system's…
Indefinite extensibility describes collections, like the set of all sets, that cannot be fully listed. Any enumeration attempt can always…
Inconsistent arithmetic refers to a mathematical system where contradictions can be proven, violating the fundamental principle of consistency. This makes…
The property of a logical or mathematical system where not all true statements can be proven within the system's own…
An implicit definition defines an entity by its relationships to other concepts rather than by direct enumeration of its properties.…
The image of a function represents the set of all possible output values derived from its input domain. It's a…
The identity function is a fundamental concept in mathematics and computer science. It's a function that takes an input and…
A hereditary property in mathematics and logic is a characteristic that, if held by an object, is also present in…