What are Natural and Whole Numbers?

Summary

Natural numbers are the numbers you can count on your hand
They start at 1 and go up by 1, going on and on forever
0 is NOT a natural number, but it IS a whole number
4/2 simplifies to 2, which IS a natural number
Negative numbers, like -6, are not natural OR whole numbers
Whole numbers are all the natural numbers plus 0
Decimals, like 1.5, are NOT whole numbers

Notes

1. When you count, you always start at 1 and go up one number at a time
2. These numbers that you use when you're counting are the natural numbers
1. Negative numbers and 0 are not natural numbers, because you can't count them on your hand
1. 2 is the number that comes after 1 when we're counting!
2. So it is the second natural number
1. If you just keep counting up from 1, you'll get all the natural numbers
1. Since you could keep counting forever if you really wanted to, the natural numbers go on forever
1. When you're counting a bunch of things, you never start with 0
2. So 0 is not a counting number
3. This means it's also not a natural number
1. If you try to count to 0, you're not actually counting anything!
1. Since you can't count to 0, it is not a natural number
1. 4/2 is a fraction
2. Does this mean it can't be a natural number?
1. If you simplify 4/2 by dividing, you end up with 2
2. Since 2 is the same thing as 4/2, that means that it IS a natural number!
1. You also don't use negative numbers when you're counting things
2. So negative numbers are not natural numbers
1. You don't use negative numbers when you're counting things
2. So negative numbers are not natural numbers
1. You don't use negative numbers when you're counting things
2. So negative numbers are not natural numbers
1. They are pretty close to the same thing
2. But the whole numbers include 0, whereas the natural numbers do not
1. So once you get past 0, the whole numbers are the same as the natural numbers
1. 0/2 is a fraction
2. Does this mean it can't be a whole number?
1. 0 over anything is just 0
2. And we know that 0 is a whole number!
1. 1.5 is a decimal
2. Decimals are NOT whole numbers
3. You don't use decimals when you count
4. So since 1.5 is not a counting number and is not 0, it is NOT a whole number
1. You don't use decimals when you count
2. So decimals are NOT whole numbers
1. -6 was not a natural number, but is it a whole number?
2. Negative numbers are not whole numbers either
3. Remember, the whole numbers are just the natural numbers and 0
4. So if it's not a natural number and not 0, then it's not a whole number
1. If we start at 0 and go up, then we don't include any negative numbers

Definition: Natural and Whole Numbers

Summary

Notes