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Aditya89
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Can anybody tell me the Canter Method of proving that certain sets are infinite? It is called as "Diagonal Method".
Aditya89 said:Hey thanks, Zurtex! But from the first link, it does not become clear why it is called "Diagonal Method". Also, can you explain the link between first proof and second proof, please?
Aditya89 said:Also, please tell me how to construct a bijection between Rationals & Reals.
The Diagonal Method, also known as Cantor's Diagonal Argument, is a mathematical proof technique used to show that a given set is infinite. It was developed by mathematician Georg Cantor in the late 19th century.
The Diagonal Method involves constructing a list of elements in a set and then creating a new element by changing each element in the list in a specific way. This new element is then shown to be different from every element in the original list, thus proving that the set is infinite.
The Diagonal Method can be used to prove that any set that contains an infinite number of elements is infinite. This includes sets of natural numbers, real numbers, and even sets of infinite sequences.
The Diagonal Method is a powerful proof technique that has been used to solve many problems in mathematics, including the famous Continuum Hypothesis. It also helps us understand the concept of infinity and the properties of infinite sets.
While the Diagonal Method is a useful tool for proving sets are infinite, it cannot be used to prove the size or cardinality of a set. It also cannot be used to prove that a set is finite, as it only works for infinite sets.