If a number like Pi is infinite, how do we know each decimal that is newly calculated is valid?

Question

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

Answer 1

>”Let’s say through thorough testing in reality, we can prove with certainty Pi is correct up until 5 decimal places”

This is the source of your confusion. Pi does not *exist* in reality. It is just a concept; the algorithms to compute it are derived by inexorable logic following from the definition of the concept.

You might think that Pi exists in reality because of its relation to circle geometry, but remember, perfect circles don’t exist in reality either.