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The idea of a group as a category with one element confuses me. Let us take the set of natural numbers. This set is a group under the operation of multiplication. Now if we consider the set of natural numbers as a group what is the one element that it will have?

I also need clarification on how the composition becomes the product.

José Carlos Santos
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Hendrix
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    $(\Bbb N,\cdot)$ is not a group. Not at all. (Only $1$ has inverse). – ajotatxe Apr 28 '19 at 10:16
  • Your general question has been asked here several times before, here is another instance. Of course, as others have remarked, $\mathbb N$ is simply not a group (under neither multiplication nor addition). – lulu Apr 28 '19 at 10:20

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It turns out that $(\mathbb N,\times)$ is not a group.

José Carlos Santos
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