MHB Real Analysis is all about infinity

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Real Analysis fundamentally explores concepts of limits, continuity, and convergence, all of which involve infinite processes. The study delves into the behavior of functions and sequences as they approach infinity, making it essential to understand these infinite aspects. Additionally, the rigorous treatment of infinite sets and cardinality is a core component of Real Analysis. This focus on infinity encourages deeper thinking about mathematical structures and their implications. Ultimately, Real Analysis challenges students to grapple with the complexities of infinite concepts in mathematics.
Tomp
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My lecturer posted a question asking why ""Real Analysis is all about infinity"

Why is this so?
 
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Tompo said:
My lecturer posted a question asking why ""Real Analysis is all about infinity"

Why is this so?

What do you think real analysis is about?

The question is mean to be provocative, to get you to think about the bigger picture of what you are studying.

CB
 

Thread 'About the definition of topological manifold using closed sets'

We all know the definition of n-dimensional topological manifold uses open sets and homeomorphisms onto the image as open set in ##\mathbb R^n##. It should be possible to reformulate the definition of n-dimensional topological manifold using closed sets on the manifold's topology and on ##\mathbb R^n## ? I'm positive for this. Perhaps the definition of smooth manifold would be problematic, though.
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