Answer:

Whole Numbers

Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, ... (and so on)

Examples: 0, 7,212 and 1023 are all whole numbers

(But numbers like ½, 1.1 and −5 are not whole numbers.)

Counting Numbers

Counting Numbers are Whole Numbers, but without the zero. Because you can't "count" zero.

number line whole

So they are 1, 2, 3, 4, 5, ... (and so on).

Natural Numbers

"Natural Numbers" can mean either "Counting Numbers" {1, 2, 3, ...}, or "Whole Numbers" {0, 1, 2, 3, ...}, depending on the subject.

Integers

Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!

number line -10 to 10

So, integers can be negative {−1, −2,−3, −4, ... }, positive {1, 2, 3, 4, ... }, or zero {0}

We can put that all together like this:

Integers = { ..., −4, −3, −2, −1, 0, 1, 2, 3, 4, ... }

Examples: −16, −3, 0, 1 and 198 are all integers.

(But numbers like ½, 1.1 and 3.5 are not integers)

The square root of 2 cannot be written as a simple fraction! And there are many more such numbers, and because they are not rational they are called Irrational.

...

Example:

Number As a Fraction Rational?

5 5/1 Yes

1.75 7/4 Yes

1000 1000/1 Yes

.001 1/1000 Yes

Irrational numbers are the real numbers that cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers.

Counting Numbers

Counting Numbers are Whole Numbers, but without the zero. Because you can't "count" zero.

number line whole

So they are 1, 2, 3, 4, 5, ... (and so on).

Step-by-step explanation:

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