Why do you think there's an infinite amount of numbers between 0 and 1? Well, 0 is a starting point for all numbers. 1 is a whole number. So how do you get to 1 starting from 0 on a number line? There's parts in between 0 and 1. These parts are parts of a whole number. 
      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. 
 





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