Carnivorous plant because light will be more limiting than nutrients. A plant can grow at zero investment in carnivory; this is also the "optimum" investment for a plant, as any investment in traps reduces net photosynthesis (growth) to less than the net photosynthesis of a plant that obtains its nutrients from soil alone. Carnivorous plants exist between these two extremes: the less limiting light and water are, and the more limiting soil nutrients are, the higher the optimum investment in carnivory, and hence the more obvious the adaptations will be to the casual observer. The most obvious evidence for this model is
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