Eutrophication may only be made available again during autumn turn-over or in conditions of turbulent flow. Enhanced growth of aquatic vegetation or phytoplankton and algal blooms disrupts normal functioning of the ecosystem, causing a variety of problems such as a lack of oxygen needed for fish and shellfish to survive. The water becomes cloudy, typically coloured a shade of green, yellow, brown, or red. Eutrophication also decreases the value of rivers, lakes and aesthetic enjoyment. Health problems can occur where eutrophic conditions interfere with drinking water treatment. Human activities can accelerate the rate at which nutrients enter ecosystems. Runoff from agriculture
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