My fellow students and I have of late been thinking upon an equivalence between the roots of rational numbers and an infinite dimensional rational vector space, which we have named

We were particularly intrigued by the possibility of defining functions of such numbers by applying linear algebra operations to their associated vectors, which we began with a brief consideration of that given by their magnitudes. We have subsequently spent some time further exploring its properties and it is upon our findings that I shall now report.

**ℓ**-space, that we discovered whilst defining analogues of logarithms that were expressed purely in terms of rationals.We were particularly intrigued by the possibility of defining functions of such numbers by applying linear algebra operations to their associated vectors, which we began with a brief consideration of that given by their magnitudes. We have subsequently spent some time further exploring its properties and it is upon our findings that I shall now report.

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