aleph-zero (Meaning)
Wordnet
aleph-zero (n)
the smallest infinite integer
Synonyms & Antonyms of aleph-zero
No Synonyms and anytonyms found
aleph-zero Sentence Examples
- Aleph-zero, often represented by the symbol ℵ₀, denotes the cardinality of countable infinity in set theory.
- Mathematicians frequently use aleph-zero to describe the size of sets that can be put into a one-to-one correspondence with the natural numbers.
- The concept of aleph-zero is fundamental in understanding the notion of countability in mathematical analysis.
- The set of all positive integers has an aleph-zero cardinality, illustrating the concept of countable infinity.
- Cantor's pioneering work in the late 19th century contributed significantly to the study of aleph-zero and transfinite numbers.
- In the context of sequences and series, aleph-zero is a critical factor in determining convergence or divergence.
- The mathematics professor elaborated on the importance of aleph-zero in foundational discussions about the nature of infinity.
- Aleph-zero is categorized as a countable infinity, differentiating it from larger cardinalities like aleph-one or aleph-two.
- The researcher's thesis delved into the properties and applications of aleph-zero within the field of mathematical logic.
- Within set theory, aleph-zero serves as a key parameter for comparing and classifying different sizes of infinite sets.
FAQs About the word aleph-zero
the smallest infinite integer
No synonyms found.
No antonyms found.
Aleph-zero, often represented by the symbol ℵ₀, denotes the cardinality of countable infinity in set theory.
Mathematicians frequently use aleph-zero to describe the size of sets that can be put into a one-to-one correspondence with the natural numbers.
The concept of aleph-zero is fundamental in understanding the notion of countability in mathematical analysis.
The set of all positive integers has an aleph-zero cardinality, illustrating the concept of countable infinity.
