Examples of 'countably infinite' in a sentence
Meaning of "countably infinite"
countably infinite: Refers to a set that can be placed into a one-to-one correspondence with the natural numbers, indicating that while infinite, the elements in the set can still be counted
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- That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection exists from ℕ to the set.
How to use "countably infinite" in a sentence
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countably infinite
Let be a countably infinite discrete group.
The number of permitted values is either finite or countably infinite.
Countably infinite set of equivalent fractions.
The set of possible output values may be finite or countably infinite.
A has a countably infinite subset.
Some authors use countable set to mean countably infinite alone.
Countably infinite is the key.
A random variable whose possible values are either finite or countably infinite.
Groups of countably infinite numbers have some interesting properties.
Normal subgroups of the sympletic group on a countably infinite dimensional vector space.
All countably infinite sets have the same cardinality.
Gödel also considered the case where there are a countably infinite collection of formulas.
The case of a countably infinite set of components is covered formally by allowing.
If the degree of the polynomials is unrestricted then the dimension of F is countably infinite.
The situation is different for countably infinite compact Hausdorff spaces.
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Every countably infinite compact K is homeomorphic to some closed interval of ordinal numbers.
Observe that N in the theorem can be replaced with any countably infinite set.
Countably infinite groups with arbitrarily small translations, rotations, or combinations.
What about infinite subsets of countably infinite sets?
Countably infinite groups without arbitrarily small translations, rotations, or combinations.
In particular, the power set of a countably infinite set is uncountably infinite.
Hence, the integers and rational numbers are also countably infinite.
Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied.
In other words, it is topologically indistinguishable from the unit cube of countably infinite dimension.
Skolem 's paradox, Countably infinite models of set theory contain uncountably infinite sets.
In some model, there is an infinite set of real numbers without a countably infinite subset.
The case of a countably infinite set of components is covered formally by allowing n ∞ { \ displaystyle n = \ infty \!
In particular, every infinite subset of a countably infinite set is countably infinite.
To understand the proof, let us examine it for the specific case when X is countably infinite.
The language of PRA consists of, A countably infinite number of variables x, y, z.
Finally, the construction ends after countably many steps because A and B are countably infinite.
In probability, a discrete distribution has either a finite or a countably infinite number of possible values.
That is, a σ-algebra is an algebra of sets, completed to include countably infinite operations.
Let Δ { \ displaystyle \ Delta } be a finite or countably infinite simplicial complex.
The Gram - Schmidt process also applies to a linearly independent countably infinite sequence { v " i " } " i ".
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Infinite forms of variations with each generation
And there are an infinite number of alternate dimensions
Infinite possibilities and all he can do is whine
