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…
Gödel's incompleteness theorems reveal fundamental limits of formal systems. They demonstrate that any consistent system powerful enough for arithmetic will…
The property of a logical or mathematical system where not all true statements can be proven within the system's own…
Inclusive first-order logic is a flexible variant that permits empty domains, unlike standard first-order logic which mandates at least one…
An impredicative definition defines an object in terms of a totality to which the object itself belongs. This can lead…
Logical implication connects two statements: if the first (antecedent) is true, the second (consequent) must also be true. It's a…
The image of a function represents the set of all possible output values derived from its input domain. It's a…
Iff, short for 'if and only if,' is a crucial logical connective indicating mutual implication. It establishes a biconditional relationship…
The identity function is a fundamental concept in mathematics and computer science. It's a function that takes an input and…