Counting Method / June 6, 2018 / Penelope Chow
Unitizing: Our number system groups objects into 10 once 9 is reached. We use a base 10 system whereby a 1 will represent ten, one hundred, one thousand etc. Of the counting principles, this one tends to cause the greatest amount of difficulty for children.
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.