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To add on to this, the question then can become why can’t the number start repeating after a certain point (e.g., 3.14133333333…). But then we can represent it
by coldcache 2y ago
To add on to this, the question then can become why can’t the number start repeating after a certain point (e.g., 3.14133333333…). But then we can represent it as a sum of 3.141 and 0.000333333…, i.e., two rational numbers. Then we can construct a fraction that represents the number.
- empath75 2y agoand it can also be shown that all rational numbers repeat because there's only so many remainders possible for a given denominator (all the numbers from 0 to n-1), and as soon as you repeat a remainder, you necessarily have to repeat everything from the last occurrence of that remainder.