Counting Numbers: the counting, or "natural" numbers:
1, 2, 3, 4, 5, 6, ...
A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways:
N = {0, 1, 2, 3, ...}
OR
N = {1, 2, 3, 4, ...}
1, 2, 3, 4, 5, 6, ...
A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways:
N = {0, 1, 2, 3, ...}
OR
N = {1, 2, 3, 4, ...}
Whole Numbers: natural numbers together with zero, denoted W, can be defined:
W = {0, 1, 2, 3, 4, 5, 6, ...}
W = {0, 1, 2, 3, 4, 5, 6, ...}
Integers: zero, the natural numbers, and the negatives of the naturals, denoted Z, can be defined:
Z = {..., –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, ...}
Z = {..., –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, 6, ...}
Rational Numbers: Fractions, denoted Q, (also known as rational numbers) can be written as terminating (ending) or repeating decimals (such as 0.5, 0.76, or 0.333333....).
Note that each new type of number contained the previous type within it. The wholes are just the naturals with zero thrown in. The integers are just the wholes with the negatives thrown in. And the fractions are just the integers with all their divisions thrown in.
Q = {x | x=a/b, a,b ∈ N}
Note that each new type of number contained the previous type within it. The wholes are just the naturals with zero thrown in. The integers are just the wholes with the negatives thrown in. And the fractions are just the integers with all their divisions thrown in.
Q = {x | x=a/b, a,b ∈ N}