Hi i was just wondering if there is any concept/theory/idea (or anything really) that relates to a growing basis (primarily in R) . What i mean by a growing basis is the following; say you start off with one element in your basis and you encounter a number/vector that cannot be built by the element, this number that cannot be built then gets incorporated into the basis and becomes an element of it and this process goes on and on picking up more building elements as it encounters numbers that cant be built from the existing elements. For example, in R, say the number you begin with is 2, then the next (integer) number you encounter is 3, which cant be built by 2, so 3 gets including in the basis. If this process were to go on and on, you would have a basis consisting of all primes (2,3,5,7,11,13,....) since all integers can be built from the primes. I hope that makes sense. Thank you!