Plant rapidly, maturing within 110 days, whereas others, in the same environmental conditions, grow more slowly and mature within 155 days. Growth is also determined by environmental factors, such as temperature, available water, available light, carbon dioxide and available nutrients in the soil. Any change in the availability of these external conditions will be reflected in the plant's growth and the timing of its development. Biotic factors also affect plant growth. Plants can be so crowded that no single individual produces normal growth, causing etiolation and chlorosis. Optimal plant growth can be hampered by grazing animals, suboptimal soil composition, lack of
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