But if at some point further decimals cannot be experimentally proven to be right, at best you can say &quot;pi is such and such for such precision&quot; and any definition that gives the same number up to that precision must be accordingly accepted. Otherwise you need to demonstrate an experiment that uses further precision.<p>But we don&#x27;t do that, and that&#x27;s why mathematics don&#x27;t have to do with experience, they are an entirely different tool that also happens to be useful in experimental science.