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Answers and Explanations

More Information on Why "Infinity" Does Exist in the Context of A Topological Space

This page provides supplementary information to the page of explanations on the question "does infinity exist?".

Remember, we are trying to see why the answer is "yes" to the following question:

Does there exist some topological space (that is, a set of objects plus a definition of what convergence means) which, as well as including the familiar real numbers we are used to, also includes an "infinity" concept to which some sequences of real numbers converge?
How do we know that a topological space with these properties really exists? Well, we just build one! Here are two ways to do it:

No matter which approach you take, you can define a topological space which has the real numbers as a subset, also has an additional object called "infinity", and in which the notion of convergence is such that sequences like 1, 2, 3, . . . converge to this additional object. In this sense, therefore, infinity exists.

This page last updated: September 1, 1997
Original Web Site Creator / Mathematical Content Developer: Philip Spencer
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