There is no such thing as **the greatest natural number**. By adding 1 to the current natural number, the next natural number may be obtained, resulting in numbers that continue on "forever." There is no such thing as **an infinite natural number**. All natural numbers up to and including 1000 have been found, but there are likely many more waiting to be discovered.

The last natural number was 433807088. It is too large to be written out in full without using a million digits. The number was first recorded by **mathematician John Napier** in his book Mirrour of Magick (1554). He called it "a very great number." It took humans about 100 years to find **its match** among the stars. The star EI Psc provides the last two digits for this number.

Natural numbers do not repeat themselves. That is, no matter how far you go back, you will never find a number that has already been counted as part of a larger number. This is because 1 every natural number can be expressed as a product of prime numbers and 2 only a finite number of prime numbers exist. Therefore, natural numbers never run out of room for more numbers.

It is possible to write down much longer numbers than those mentioned above and still not cover them all.

There is no fixed smallest natural number and no set greatest natural number. However, we can say that any natural number greater than or equal to 2 is both smaller and larger than **any single natural number**.

In mathematics, a natural number is any number that results from counting objects of **a same type**, such as people or animals. There are many different ways of counting, and thus there are many different ways of defining what natural numbers are. For example, some count **only whole numbers** while others include fractions.

The study of **natural numbers** began with an attempt to understand how to count accurately. It is assumed that if you want to count accurately you need to know how to identify individual objects. If you cannot do this, then it is impossible to count accurately and therefore to define what natural numbers are.

Natural numbers are important in mathematics because they appear everywhere you would expect to find them: in arithmetic problems, in calculus problems, and in analysis problems. In fact, calculus problems often ask you to determine whether or not a function is one-one or onto. A function is one-one if its inverse image of every element in its domain is always just one other element.

Natural numbers consist of the integers 1, 2, 3, and 4.. They are the numbers you normally count, and they will go on indefinitely. Whole numbers are all natural numbers, including 0; for example, 0, 1, 2, 3, 4, and so on. Half numbers are the integers except for 0 and 5; for example, -1, 0, 1, 2, 3, and so on.

Counting numbers are a subset of the natural numbers that includes 0, 1, 2, 3, and so on, up to some number you decide. For example, you can count from 1 to 10 as quickly as you like but once you get to 10 you should stop because there are more than 10 things you could do next. Or you can count down from 100 to 1 which is the same as counting from 1 to 100 because 100 comes after 1 in any case.

0 is not a counting number because there is no such thing as zero or negative numbers in general, only differences. If you subtract one counting number from another then there must be a unique result that is also a counting number. For example, if I say "I counted to 10" then this means I counted from 1 to 10 without stopping, and since 10 is a counting number this means I had to stop at some point during **my count**.

A natural number is an integer that is bigger than zero. Natural numbers start at one and go up to infinity: 1, 2, 3, 4, 5, and so on. Natural numbers are often known as "counting numbers" since they can be counted. There are also positive integers that aren't counting numbers because three is a bound there. These numbers are called "finite" or "non-counting." There are no finite numbers before two because all the numbers up until then are counting numbers.

Finite numbers end with two reasons: first, it's because after **that point** you'll run out of things to count (or dice to roll), and second, because including those numbers will make arithmetic difficult (3 + 4 = 7 instead of 8). Infinite numbers continue forever in both directions without **any limit** other than the limits of mathematics itself. Since we know that there must be some higher number, it follows that infinite numbers must start somewhere.

Infinity is a very abstract concept and it's hard to understand exactly what it means. We can say that infinity is more than **any single number** and less than another number. It's like having millions of dollars but not being able to spend a single dollar.