transfinite Definition
- 1extending beyond finite numerical values or limits
- 2denoting a number greater than any finite number
Using transfinite: Examples
Take a moment to familiarize yourself with how "transfinite" can be used in various situations through the following examples!
Example
Cantor's transfinite numbers revolutionized the study of infinity.
Example
Transfinite sets are used in set theory to describe infinite collections of objects.
Example
The concept of transfinite arithmetic is central to Cantor's work on infinity.
transfinite Synonyms and Antonyms
Phrases with transfinite
a mathematical proof technique used to prove statements about transfinite ordinal numbers
Example
Transfinite induction is a powerful tool for proving theorems in set theory.
a set that is either finite or has the same cardinality as a proper subset of itself
Example
The set of natural numbers is a transfinite set.
a method of defining a function on the transfinite ordinal numbers by specifying its values at smaller ordinals
Example
Transfinite recursion is used to define functions on transfinite sets.
Origins of transfinite
from Latin 'trans-', meaning 'beyond', and 'finite'
Summary: transfinite in Brief
'Transfinite' [trans-fahyn-ahyt] refers to extending beyond finite numerical values or limits, often denoting a number greater than any finite number. It is a term used in mathematics to describe concepts such as transfinite sets, transfinite induction, and transfinite recursion. Examples of its usage include 'Cantor's transfinite numbers revolutionized the study of infinity.'
