If we’re measuring a length of pi centimeters, why does it look finite but the number of digits is going on forever? It looks like that it’s moving small amount of time every time. Same with 0.5555555… or any number with infinite decimal places. I can’t wrap my head around it.
In: 0
It seems the confusion here is stemming from imagining that each new digit is adding on to the length. That would be incorrect. Each new digit is increasing the *accuracy*.
We measure a string with a length of pi. It’s a bit more than 3 but a lot less than 4 so we add a decimal. Now we measure and the same string is a more than 3.1 but less than 3.2. We still don’t accurately have the string measured, so we add another decimal. It looks like the *same string* is longer than 3.14 but less than 3.15.
We can continue this indefinitely, but the key is that the string we are measuring stays exactly the same length. Our ability to measure it accurately changes as we keep adding digits, but fundamentally it’s no different than just measuring something that is exactly 3.0000000…. We can keep measuring it and adding on zeros to confirm that it isn’t 3.00…1, but adding an infinite number of zeros (or other digits in the case of pi) doesn’t conflict with the thing we are actually measuring being finite.
Latest Answers