eli5 Is there a reason that the decimals of pi go on forever (or at least appear to)? Or do it just be like that?

Question

Edit: Thanks for the answers everyone! From what I can gather, pi just do be like that, and other irrational numbers be like that too.

In: 5168

Answer 1

While answers like “it just be like that” are certainly true, I find it helpful to think of irrational numbers like pi as infinite series rather than specific magic numbers.

If you think of pi as the Leibniz formula i.e 4(1-1/3+1/5-1/7+…), you can sort of see how its computation may lead to infinite decimals as you add up more terms to infinity. Infinite series won’t always converge or converge to irrational numbers, but in this case it does.