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Are all infinite sets equal according to one to one correspondence?
Wiki User
∙ 10y ago
No.
The "smallest" infinity is the cardinality of the natural numbers, N. This cardinality is named Aleph-null. Rational numbers also have the same cardinality as do n-tuples of rational numbers.
The next larger cardinality is that of the real numbers. This is the "continuum, C, which equals 2aleph-null. As with the cardinality of the natural numbers, n-tuples of reals have the same cardinality.
The point about introducing n-tuples, is that they are used to denote points in n-dimensional space.
If you want more read some of the Wikipedia articles of Cantor, Hilbert's Grand Hotel. These could lead you to many more related articles - though sadly, not infinitely many!
Wiki User
∙ 10y ago
No, all infinite sets are not necessarily equal according to one-to-one correspondence. One-to-one correspondence is a way to compare and classify infinite sets based on their cardinality. Sets that have a one-to-one correspondence are said to have the same cardinality, which means they are equal in size. However, not all sets have the same cardinality. For example, the set of natural numbers (countably infinite) has a different cardinality than the set of real numbers (uncountably infinite).
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What is the kinds of sets?
Closed sets and open sets, or finite and infinite sets.
What are kind of set?
There are finite sets, countably infinite sets and uncountably infinite sets.
Kinds of sets and its example?
Sets are collection of distinct objects. In mathematics there are different types of sets like Finite set, Infinite set, Universal set, subset, equal set, equivalent set. Example of Finite set {1,2,3,4}. Infinite set:{1,2,3....}.
What are three examples of infinite sets?
stars in the sky that's the some example of infinite sets
What is the two kind of sets?
Closed sets and open sets, or finite and infinite sets.
What are the examples of equal set?
Two sets are equal if they contain the same identical elements. If two sets have only the same number of elements, then the two sets are One-to-One correspondence. Equal sets are One-to-One correspondence but correspondence sets are not always equal sets.Ex: A: (1, 2, 3, 4)B: (h, t, m, k)C: (4, 1, 3, 2)A and C are Equal sets and 1-1 correspondence sets.
What are the example of Equality?
Two sets are equal if they contain the same identical elements. If two sets have only the same number of elements, then the two sets are One-to-One correspondence. Equal sets are One-to-One correspondence but correspondence sets are not always equal sets.Ex: A: (1, 2, 3, 4)B: (h, t, m, k)C: (4, 1, 3, 2)A and C are Equal sets and 1-1 correspondence sets.
All infinite sets are not equal?
Absolutely not
What are kinds of sets according to number of elements what are kinds of sets according to number of elements?
Finite, countably infinite and uncountably infinite.
What are the kinds of sets according to number of elements?
One possible classification is finite, countably infinite and uncountably infinite.
What is the kinds of sets?
Closed sets and open sets, or finite and infinite sets.
What are kind of set?
There are finite sets, countably infinite sets and uncountably infinite sets.
Kinds of sets and its example?
Sets are collection of distinct objects. In mathematics there are different types of sets like Finite set, Infinite set, Universal set, subset, equal set, equivalent set. Example of Finite set {1,2,3,4}. Infinite set:{1,2,3....}.
What are three examples of infinite sets?
stars in the sky that's the some example of infinite sets
What is the two kind of sets?
Closed sets and open sets, or finite and infinite sets.
Are sets always infinite?
No.
What is kind of set?
Closed sets and open sets, or finite and infinite sets.
