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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!

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11y ago
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8mo 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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Q: Are all infinite sets equal according to one to one correspondence?
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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.


What is the difference between natural infinite and real infinite set?

A Natural infinite set refers to one whose members can be put into 1-to-1 correspondence with the natural numbers, while a real infinite set is one whose members can be put into 1-to-1 correspondence with the real numbers. Although both sets are infinite, they are not of the same cardinality (size).The cardinality of the natural infinite set is denoted by À0 or Aleph-null. The cardinality of the real infinite set is 2 to the power À0, which is denoted by C. (Actually Aleph looks like an N with wriggly lines but this browser is incapable of displaying it.)For more on the cardinality of infinite sets, see the related links. Georg Cantor's diagonal argument is exquisite - simple but immensely powerful. If you want to get a feel for transfinite arithmetic - read about Hilbert's Hotel paradox.


Are sets always infinite?

No.