In Ancient Greek, most people like Pythagoras thought 1(monad, unity) is no number, but it is ruler and beginning of all other numbers. And Pythagoras thought everything is number. But they found irrational number which can not be measured by 1, and their theory broke up because of it. But even though ancient Greek found irrational numbers, for example, Euclid who was born after Pythagoras and also knew about irrational number, said every number is made by 1(monad). Not only Ancinet Greek, but also Medium aevum arthimetician says 1 is source of all other numbers.
Q1. Why did they say 1 is source of numbers even though they found existence of irrational numbers? Is it because they only treated natural numbers as number?
Q2. If so, (Only natural numbers can be number) what was irrational number for them? C
Q3. According to ancient Greeks, If 'one' can not be divided, how fraction can be exist? (1/2 or 1/3 etc..)