Hi, I've got a project at uni and part of it is this proof by induction which i am terrible at. I can never work out where to sub in n+1 or n+2 n-1 or whatever it may be so any help much appreciated!!
An affine subset of is a non-empty subset of with the property that whenever and
i) Let be an affine subset of . Prove by induction on that, if and with , then
belongs to .
ii) A sum of the form (1) is called an affine combination of . Prove that, given a non-empty subset of , the set consisting of all afine combinations of elements of is an affine subset of and is the smallest affine subset of containing . This set is called the affine span of .