aleph-null (Meaning)
Wordnet
aleph-null (n)
the smallest infinite integer
Synonyms & Antonyms of aleph-null
No Synonyms and anytonyms found
aleph-null Sentence Examples
- Aleph-null, often denoted as ℵ₀, represents the cardinality of countable infinity in set theory.
- Mathematicians frequently use aleph-null to describe the size of infinite sets, particularly those that can be put into a one-to-one correspondence with the natural numbers.
- Aleph-null plays a central role in understanding the concept of countability in mathematical analysis.
- The set of integers has the same cardinality as aleph-null, illustrating the concept of countable infinity.
- Cantor's work in the late 19th century paved the way for a deeper understanding of aleph-null and transfinite numbers.
- When dealing with sequences and series, aleph-null is a key parameter in determining convergence or divergence.
- The mathematics professor explained the significance of aleph-null in foundational discussions about the nature of infinity.
- Aleph-null is considered a countable infinity, distinct from larger cardinalities such as aleph-one or aleph-two.
- The researcher's paper focused on the properties and applications of aleph-null within the realm of mathematical logic.
- In set theory, aleph-null is crucial for comparing and categorizing different sizes of infinite sets.
FAQs About the word aleph-null
the smallest infinite integer
No synonyms found.
No antonyms found.
Aleph-null, often denoted as ℵ₀, represents the cardinality of countable infinity in set theory.
Mathematicians frequently use aleph-null to describe the size of infinite sets, particularly those that can be put into a one-to-one correspondence with the natural numbers.
Aleph-null plays a central role in understanding the concept of countability in mathematical analysis.
The set of integers has the same cardinality as aleph-null, illustrating the concept of countable infinity.
