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I suppose this question can be interpreted in two ways. It is often the case that two or more equivalent (but not necessarily semantically equivalent) definitions of the same idea/object are used in ...

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but we rarely talk about ...

Can you make an example of a great proof by induction or construction by recursion? Given that you already have your own idea of what "great" means, here it can also be taken to mean that the chosen ...