Counting Method / June 6, 2018 / Penelope Chow
A child's first teacher is their parent. Children are often exposed to their earliest math skills by their parents. When children are young, parents use food and toys as a vehicle to get their children to count or recite numbers. However, the focus tends to be on rote counting, always starting at number one rather than the understanding the concepts of counting. As parents feed their children, they will refer to one, two, and three as they give their child another spoonful or another piece of food or when they refer to building blocks and other toys. All of this is fine, but counting requires more than a simple rote approach whereby children memorize numbers in a chant-like fashion. Most of us forget how we learned the many concepts or principles of counting.
Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers, and, importantly, 0, Z (unlike the natural numbers) is also closed under subtraction. The integers form a unital ring which is the most basic one, in the following sense: for any unital ring, there is a unique ring homomorphism from the integers into this ring. This universal property, namely to be an initial object in the category of rings, characterizes the ring Z.