Does pi go on forever ? How do we know ?

@CheekyBadger not all? 0.5 does not go on forever

@Evolved 0.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

I would go on but I’m in an iPad!

We just pick a convenient point to say stuff it and don’t write any more.

@CheekyBadger That is equivalent to 0.5 . So don't see your point. Certain decimal point are not recurring. When it goes on forever it becomes recurring.

@Evolved I'm just giving an illustration of how inadequate decimal numbers are really for describing stuff. Recurrance just affects a subset of decimal numbers (e.g. 1/3) but ultimately we decide to accept an arbitary degree of precision when using them. Some numbers work nicely - e.g 0.5 where we have a high degree of precision but others not so much (like pi). Pi doesn't result from a ratio between two numbers and is considered irrational. These types of numbers are infinitely long in expression and don't contain recurrance. It helps to think of all decimal numbers as infinitely long (as they are) but in the "nice" cases it is 0 that makes up the bulk.

@CheekyBadger Thank you for your answer, but .5 is .5 only. It has no recurrence as zero is not counted even if it goes on forever. 1/3 is recurring and is regarded to go on forever like pi does. My question is how do we know that recurrence is infinite .

@Evolved Unfortunately I'm not a mathematician so lack the ability to describe it exactly - if you look at https://en.m.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational it will give some details - irrational numbers have the property of being infinitely long too.

@CheekyBadger Sorry my question was a bit mathematical. Thank you for the link.

@CheekyBadger Adding zeros doesn’t change the accuracy of 0.5 but adding another 3 to 0.333… does.

The difference between how we express 1/2 and 1/3 depends on our base 10 number system. They are both rational numbers because they can both be written as a fraction with two integers whereas Pi can’t