There are lots of ways to define "more" (or "bigger" or whatever term one chooses to use). Which one is most appropriate depends on what kind of things you're w

There are lots of ways to define "more" (or "bigger" or whatever term one chooses to use). Which one is most appropriate depends on what kind of things you're working with. Working with vector spaces over a given field: "bigger" means "higher dimension". Working with manifolds: "bigger" means "higher dimension". Working with sets: "bigger" usually means "larger cardinality" but could sometimes mean "proper superset". In general, you can take "X is bigger than Y" to mean "Y is isomorphic to some substructure of X, but not vice versa". If "isomorphic" means "in bijection with" and "substructure" means "subset" then this is cardinality. If they mean "isomorphic as vector spaces over F" and "vector subspace" then it's dimension. If they mean "homeomorphic" and "topological subspace" then actually it isn't true that lower-dimensional manifolds are always "smaller than" higher-dimensional ones (so maybe we actually want a different definition) but in this particular case the rank-1 tensors are a lower-dimensional proper subspace of all the tensors so the definition gives the "right" answer.