In mathematics, a 4-digit odd number is an integer composed of four distinct odd digits. These numbers are sometimes referred to as natural numbers, which means they are not negative or fractional. The range of 4-digit odd numbers is limited to 10,000, since the largest possible number with 4 digits is 9999.

## Counting 4-Digit Odd Numbers

The number of 4-digit odd numbers is relatively straightforward to calculate. The first digit can be any of the nine odd digits, from 1 to 9. The second digit can be any of the eight remaining odd digits, from 1 to 9, and so on. This means that the total number of 4-digit odd numbers is 9 x 8 x 7 x 6, which is 3,024.

## Distinct and Natural Numbers

It is important to note that all 4-digit odd numbers are both distinct and natural. This means that each digit in the number is different, and the number is not negative or fractional. For example, 1357 is a 4-digit odd number, and each of its digits is different, and it is a natural number.

In conclusion, 4-digit odd numbers are composed of four distinct odd digits. The total number of 4-digit odd numbers is 3,024, and each number is both distinct and natural.

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