I know that some computers have calculated up to trillions of digits, but how do we know that it just doesn’t end at sone point?
In: Mathematics
think of a circle.
to know how the circumfence of this circle is, you need to use pi.
to almost reach the circumfence of this circle, you can put in a hexagon or octagon. the more corners you add, the more accurate it is. The closer it becomes a circle.
but, to make something absolutely like a circle, so perfectly round, you’d need an infinite amount of corners
every digit in Pi is basically one corner space.
Some very very clever people didn’t know either, so they though it wasn’t infinite. But THEN they tried using it and it made no sense! The very very clever people knew then that it was infinite.
1. We’ve proven that pi is irrational. An irrational number is one that can’t be represented as the ratio between two whole numbers.
https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
The proof itself is unfortunately too complicated for ELI5.
2. We’ve proven that if a number’s decimal expansion is repeating, then it is rational. For example, if x=0.123123123… Then 1000x=123.123123123…, so we can calculate 1000x-x = 123, therefore x=123/999, i.e. x is rational. Therefore, if a number is irrational, its decimal expansion must be infinite and non repeating.
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