numbers also called natural numbers?

Question

i was just wondering what numbers are also called natural numbers. i can't remember lol

Answer 1

I believe they're called counting numbers.

Answer 2

The expression "natural numbers" is used less and less in mathematics because it can mean two things:

The list of counting numbers (1, 2, 3, 4...) or the list of non-negative integers (0, 1, 2, 3, 4...). I've just finished a degree in math and, depending on the topic, "Big N" as we call it sometimes means the first set and sometimes the second set. Go figure...

We now prefer to "say what we mean" (even though some are still confused by the first two):

Positive integers = 1, 2, 3, 4....
Non-negative integers = 0, 2, 3, 4...
Integers = ... -4, -3, -2, -1, 0, 1, 2, 3, 4...

Some people, just to be certain, will call the first one Strictly Positive Integers. This explicitly excludes the zero.


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Natural numbers were associated with counting numbers. In Set theory, there exists an "empty set" and when you "count" the number of elements it contains, you get zero. It is the only set with that property. Nonetheless, this formalised the use of zero as a counting number back in the 19th century. Hence the confusion.

BTW:
The set {0} is not an empty set. It contains one element.

Answer 3

In mathematics, a natural number can mean either an element of the set {1, 2, 3, ...} (i.e the positive integers or the counting numbers) or an element of the set {0, 1, 2, 3, ...} (i.e. the non-negative integers). The former is generally used in number theory, while the latter is preferred in mathematical logic, set theory and computer science. See below for a formal definition.

Natural numbers have two main purposes: they can be used for counting ("there are 3 apples on the table"), and they can be used for ordering ("this is the 3rd largest city in the country").

Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting, such as Ramsey theory, are studied in combinatorics.

Answer 4

The natural numbers are the 'natural' counting numbers- 1,2,3,4,5,6,7,8... i.e. the positive integers.

Note that 0 is NOT a natural number.