Lake Erie eutrophication, in which additional nitrogen and phosphorus enter the lake, will cause plant life to "run wild and multiply like crazy". Since there are fewer wetlands, which are like "Nature's kidneys" by filtering nutrients, as well as greater "channelization of waterways", nutrients in water can cause algal blooms to sprout as well as "low-oxygen dead zones" in a complex interaction of natural forces. As of the 2010s much of the phosphorus in the lake comes from fertilizer applied to no-till soybean and corn fields but washed into streams by heavy rains. The algal blooms result from growth of Microcystis, a
Proofs involving the addition of natural numbers 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 Peano axioms for the definitions of addition of the natural numbers, and the successor function S(a). In particular: For the proof of commutativity, it is useful to define another natural number closely related to the successor function, namely "1". We define 1 to be the successor of 0, in other words, Note that for all natural numbers