Not a mathematician here at all so perhaps my question is phrased incorrectly.
Let’s say through thorough testing in reality, we can prove with certainty Pi is correct up until 5 decimal places,
3.14159
The computers that are calculating Pi to an endless degree, how do they validate new values that are calculated as correct and cannot be otherwise?
In: 434
It’s like a game of hot/cold that you played as a kid.
Suppose you start off somewhere in the country playing a game of hot and cold. When you get closer, someone tells u are warmer, and when u get further, someone says you are colder. Your target could be anywhere in the country when you start.
You start in new york. After a while, you realize that you are only getting hotter when you head west. Eventually, after many rounds, you end up in seattle. After more rounds you narrow it down to a specific neighboorhood, to a specific house, and finally to a specific room. Now, you don’t know where it is yet, but you know it’s in this room, cause whenever you are outside the room they say you are getting colder.
Now, after all this work, someone comes to you and asks -how do you know it’s not in florida? The answer is obvious to you. Well, it’s the same way that we know the first digit of pi is a 1. We have a formula that gets us closer and closer to the answer the more we use it – and after you have gotten 10 digits in deep, you know the answer isn’t in florida any more.
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