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JamesOrland
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I was wondering. Has anyone ever been able to build a beth-2 set? What does it look like? What could it possibly look like?
JamesOrland said:I was wondering. Has anyone ever been able to build a beth-2 set? What does it look like? What could it possibly look like?
In mathematics, cardinality refers to the size or number of elements in a set. When we say "cardinality bigger than that of the reals", we are referring to a set that has more elements than the set of real numbers, which is infinite.
Yes, there are sets with a larger cardinality than the real numbers. One example is the set of all possible subsets of the real numbers, also known as the power set. This set has a cardinality that is greater than that of the real numbers.
The cardinality of a set is determined by counting the number of elements in the set. For finite sets, this is a straightforward process. For infinite sets, the cardinality is determined using a mathematical concept called bijection, which involves finding a one-to-one correspondence between the elements of two sets.
Yes, the cardinality of the reals can be exceeded by an infinite set. As mentioned before, the power set of the real numbers has a larger cardinality than the real numbers themselves.
Cantor's continuum hypothesis is a mathematical conjecture that states that there is no set with a cardinality between that of the natural numbers and the real numbers. The concept of "cardinality bigger than that of the reals" is closely related to this hypothesis, as it involves sets with a cardinality larger than that of the reals. However, the continuum hypothesis has been proven to be independent of standard set theory, so it cannot be definitively answered.