Definition
Counting number
In AXIO, counting numbers are the positive integers 1, 2, 3, and so on.
Continue from this idea into connected AXIO math.
Boundary check: This glossary starts counting numbers at 1; zero is shown only as the boundary.
What it means
Counting numbers are the numbers you say when counting one or more objects. Start at 1, then keep adding 1. AXIO does not include 0 in this term, although some sources use a different convention.
Remember it
Start at one and keep stepping by one.
Example
A box holds 32 pencils. The count 32 is a counting number because it appears in 1, 2, 3, … . Zero and −3 are not counting numbers under this convention.
Watch for
The phrase “natural number” is not a safe shortcut here because some conventions include 0 and others do not.
Common mix-up
Whole numbers include 0; AXIO’s counting numbers begin at 1.
Exact meaning
In this glossary, a counting number is a positive integer: one of 1, 2, 3, … . The sequence starts at 1 and continues without end.