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I'm self-teaching maths to preper myself for the next term of uni, so I'm reading this book on abstract algebra, and somewhere it says that R (the set of real numbers) is not finitely generated as a module over Q (set of rational numbers). Now, I can see that it's not, but i can't think of a rigorous proof for it. I thought maybe i hould just find a countr example like i did in a different case (Q is not finitely ggenerated over Z) but i'm prety bad at these counter examples! lol. Can anyone help me make sense of this? cause i prefer to understand everything before i continue to the next part.

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# Q as a module over Z

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