Eutrophication Eutrophication Eutrophication (from Greek "eutrophos", "well-nourished"), or hypertrophication, is when a body of water becomes overly enriched with minerals and nutrients that induce excessive growth of plants and algae. This process may result in oxygen depletion of the water body. One example is the "bloom" or great increase of phytoplankton in a water body as a response to increased levels of nutrients. Eutrophication is almost always induced by the discharge of nitrate or phosphate-containing detergents, fertilizers, or sewage into an aquatic system. Eutrophication arises from the oversupply of nutrients, which leads to overgrowth of plants and algae. After such organisms
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