Sodium triphosphate (due to hydrolysis), no studies have been carried out to date concerning the chronic effects of STPP on these aquatic organisms. Predicted no-effect concentrations were therefore calculated for the aquatic environment and sediments on the basis of the acute aquatic ecotoxicity results. Detergents containing phosphorus contribute, together with other sources of phosphorus, to the eutrophication of many fresh waters. Eutrophication is an increase in chemical nutrients—typically compounds containing nitrogen or phosphorus—in an ecosystem. It may occur on land or in water. The term is, however, often used to mean the resultant increase in the ecosystem's primary productivity (excessive plant growth
Proofs involving the addition of natural numbers induction on "a", and so we have proved the base case "b" = 1. Now, suppose that for all natural numbers "a", we have "a" + "b" = "b" + "a". We must show that for all natural numbers "a", we have "a" + "S"("b") = "S"("b") + "a". We have This completes the induction on "b". Proofs involving the addition of natural numbers This article contains mathematical proofs for some properties of addition of the natural numbers: the additive identity, commutativity, and associativity. These proofs are used in the article Addition of natural numbers. This article will use the