These parts, or numbers, are usually written as fractions or decimals. The numbers that are between 0 and 1 go on forever because it is usually greater than 0 but less than 1. For example, the decimal .01 is greater than 0 but less than 1. If you keep adding 0's to the 1 or any other number, it will still be between 0 and 1. And there are an infinite amount of numbers for that. All these parts will make 1 whole. So then, between 1 and 2, there are also parts. It is also the same with 2 and 3, 3 and 4, 4 and 5, etc. The possiblities of numbers between 0 and 1 are endless, therefore the list goes on forever. The numbers that are infinite between 0 and 1 are parts of a whole, also known as fractions. This is my explaination for why there are an infinite amount of numbers between 0 and 1.