riz ed ▁by ▁ ▁as : ▁ ▁with ▁the ▁special ▁point ▁( 0 , 0 ) ▁corresponding ▁to ▁t ▁= ▁ 0 . ▁Now ▁define ▁ ▁as ▁the ▁order ▁of ▁the ▁formal ▁power ▁series ▁in ▁ ▁obtained ▁by ▁restriction ▁of ▁any ▁non - zero ▁polynomial ▁ ▁to ▁the ▁curve ▁: ▁ ▁This ▁extends ▁to ▁the ▁field ▁of ▁rational ▁functions ▁ ▁by ▁, ▁along ▁with ▁. ▁ ▁Some ▁intersection ▁numbers : ▁ ▁Vector ▁spaces ▁over ▁valu ation ▁fields ▁Suppose ▁that ▁▁ ∪ ▁{ 0 } ▁is ▁the ▁set ▁of ▁non - negative ▁real ▁numbers ▁under ▁multiplication . ▁Then ▁we ▁say ▁that ▁the ▁valu ation ▁is ▁non - dis crete ▁if ▁its ▁range ▁( the ▁valu ation ▁group ) ▁is ▁infinite ▁( and ▁hence ▁has ▁an ▁accum ulation ▁point ▁at ▁ 0 ). ▁ ▁Suppose ▁that ▁X ▁is ▁a ▁vector ▁space ▁over ▁K ▁and ▁that ▁A ▁and ▁B ▁are ▁subsets ▁of ▁X . ▁Then ▁we ▁say ▁that ▁A ▁absor bs ▁B ▁if ▁there ▁exists ▁a ▁α ▁ ∈ ▁K ▁such ▁that ▁ λ ▁ ∈ ▁K ▁and ▁| λ | ▁ ≥ ▁| α | ▁implies ▁that ▁B ▁ ⊆ ▁ λ ▁A . ▁A ▁is ▁called ▁radial ▁or ▁absor bing ▁if ▁A ▁absor bs ▁every ▁finite ▁subset ▁of ▁X . ▁Rad ial ▁subsets ▁of ▁X ▁are ▁invariant ▁under ▁finite ▁intersection . ▁ ▁Also , ▁A ▁is ▁called ▁circ led ▁if ▁ λ ▁in ▁K ▁and ▁| λ | ▁ ≥ ▁| α | ▁implies ▁ λ ▁A ▁ ⊆ ▁A . ▁The ▁set ▁of