Recent content by Simon-M

There are arbitrarily large gaps in the prime numbers. This means that \pi(n) can be constant over an arbitrarily large interval. Consider the n-1 numbers n!+k[/itex] where [itex]k=2,3,\cdots n

There is a difference between creating a bijection between a set and a bijection between vector spaces. Sure, we could "number" them all, but it wouldn't be a great "representation" as it wouldn't even respect addition

Only in 1D, yes. Assuming your definitions are: "A vector is a quantity with 'magnitude' and 'direction'" "A number is a real number" When working in 1D we can show 'direction' with the sign of the number. That's all I was saying. Going along the lines of a bijection between the reals and...

The "sign" of a number could act as a "direction" (using your definition of a vector)