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transfinite
This term is a specialized technical expression used almost exclusively within the domain of set theory and higher mathematics. It describes a specific category of infinity that transcends the finite, distinguishing between different "sizes" of infinite sets, such as the difference between the set of natural numbers and the set of real numbers.
When used as a noun, it refers to a specific transfinite number. While the word can be pluralized in a mathematical context to discuss various transfinite cardinals or ordinals, it is rarely used in general conversation or non-academic writing due to its highly specific logical requirements.
Meanings
Examples
The professor explained the properties of transfinite numbers during the lecture.
Is it possible to have a transfinite set that is smaller than another infinite set?
He spent hours pondering the nature of the transfinite.
Transfinite induction allows us to prove statements for all ordinal numbers.
The concept of transfinite cardinals revolutionized our understanding of infinity.
The concept of transfinite cardinals revolutionized our understanding of infinity.
I wonder if there is a limit to how many transfinite levels exist.
We are studying the hierarchy of transfinite ordinals this semester.
The proof relies on the existence of a transfinite sequence of operations.