Assume A is a set and define $\alpha$ to be the set of ordinals dominated by A. Show that (iii) $\alpha$ is the least cardinal greater than card A.
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(Enderton set theory) Hartog's theorem and cardinal numbers
17987
Which of the following sets has the greatest cardinality?(Math subject GRE exam 0568 Q.61 )
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Prove that for any set $A$ there is some $x \notin A$
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$|A\times B|= \text{max}(|A|,|B|)$ for infinite sets
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Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
154356
The "difference" of two ordinals
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Why are infinite cardinals limit ordinals?
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The cardinality of the set of all finite subsets of an infinite set
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What is the cardinality of the set of the empty set?
132298
How do you find the smallest of homeomorphic ordinals?
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Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
32081
The dual version of trichotomy of cardinality without AC
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Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$
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The statement "$\alpha$ is a cardinal" is not absolute
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Cardinality of a set that consists of all existing cardinalities
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Prove that $1^\alpha + 2^\alpha = 3^\alpha $ if $ \alpha $ is a limit ordinal
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Why is the cardinality of set S is 3^n, where S is the collection of all ordered pairs of disjoint subset of {1,2,3,...,n} where n is non negative.