mathematics

Infinitesimal: Understanding Non-Standard Analysis

An infinitesimal is a quantity approaching zero but not zero, crucial in non-standard analysis. It allows for rigorous calculus using…

4 days ago

Inductive Step in Mathematical Induction

The inductive step of a proof by induction demonstrates that if a property holds for any arbitrary element 'n', it…

4 days ago

Independence Results in Logic and Mathematics

An independence result demonstrates that a statement is neither provable nor disprovable within a specific axiomatic system, assuming the system's…

4 days ago

Indefinite Extensibility

Indefinite extensibility describes collections, like the set of all sets, that cannot be fully listed. Any enumeration attempt can always…

4 days ago

Inconsistent Arithmetic: When Logic Fails

Inconsistent arithmetic refers to a mathematical system where contradictions can be proven, violating the fundamental principle of consistency. This makes…

4 days ago

Incompleteness in Logic and Mathematics

The property of a logical or mathematical system where not all true statements can be proven within the system's own…

4 days ago

Implicit Definition

An implicit definition defines an entity by its relationships to other concepts rather than by direct enumeration of its properties.…

4 days ago

Image in Mathematics: Definition and Concepts

The image of a function represents the set of all possible output values derived from its input domain. It's a…

4 days ago

The Identity Function: Understanding Input and Output

The identity function is a fundamental concept in mathematics and computer science. It's a function that takes an input and…

4 days ago

Hereditary Property

A hereditary property in mathematics and logic is a characteristic that, if held by an object, is also present in…

4 days ago