A subset "S" of "L" is a transcendence basis of "L" /"K" if it is algebraically independent over "K" and if furthermore "L" is an algebraic extension of the field "K"("S") (the field obtained by adjoining the elements of "S" to "K"). One can show that every field extension has a transcendence basis, and that all transcendence bases have the same cardinality; this cardinality is equal to the transcendence degree of the extension and is denoted trdeg"K" "L" or trdeg("L" /"K").