Plant perception (physiology) auxin redistribution occurs in a way to produce differential growth away from gravity. For perception to happen, the plant must sense, perceive and translate the direction of gravity. Without gravity, proper orientation will not occur and the plant will not effectively grow. The root will not be able to uptake nutrients or water, and the shoot will not grow towards the sky to maximize photosynthesis. Plants do not have a brain or neuronal network, but reactions within signalling pathways may provide a biochemical basis for learning and memory in addition to computation and problem solving. Controversially, the brain is used
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