Plant tolerance to herbivory affect plant growth and also tolerance are water, light, carbon dioxide and soil nutrients. Water and light levels are generally assumed to be positively associated with tolerance (Strauss and Agrawal 1999). However, there are exceptions such as evidence of decreased tolerance in "Madia sativa" with increased water availability (Wise and Abrahamson 2007, Gonzales "et al." 2008). Many studies have found CO levels to decrease tolerance in plants (Lau and Tiffin 2009). Increased nutrient levels are also commonly found to be negatively associated with tolerance (Wise and Abrahamson 2007). There are currently three prominent models that predict how resource levels may
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