Definition:Transfinite Ordinal
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Definition
Let $\alpha$ be an ordinal.
Then $\alpha$ is said to be transfinite if and only if it is an infinite set.
Countable Ordinal
Let $\alpha$ be an ordinal.
Then $\alpha$ is said to be countable if and only if it is a countable set.
Uncountable Ordinal
Let $\alpha$ be an ordinal.
Then $\alpha$ is said to be uncountable if and only if it is an uncountable set.
Also known as
A transfinite ordinal is also known as an infinite ordinal.
Also see
Sources
- 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): Appendix $\text{A}$: Set Theory: Natural and Ordinal Numbers