Suppose we label all the vertices of a rooted tree T with numbers. These labels obey the property that every vertex has a label larger than the labels of its children (the vertices that it’s connected to below it). Prove by structural induction that the root has the largest label in the tree.

In  mathematics, the  pythagorean theorem, also known as  pythagoras' theorem, is a fundamental relation in  euclidean geometryamong the three sides of a  right triangle. it states that the square of the  hypotenuse  (the side opposite the  right angle) is equal to the sum of the squares of the  other two sides. the  theorem  can be written as an  equationrelating the lengths of the sides  a,  b  and  c, often called the "pythagorean equation".