Not sure why you are asking me these types of questions but if you're interested; I'm not swimming in vodka right now so lets try this..
Pi is irrational. If it wasn't then a circle at an eventual resolution would have to be made up of straight lines. This is not the case, of course. Meaning that Pi is basically irrational to infinity.
That's the mathmatics of it.
But for a circle drawn to a finite size its possible to specify a segment length where the segment is indistinguishable from a straight line. Thats Planck length. so the expression of the ratio of the circle's circumference to its diameter will have a limit to its consequential accuracy.
"Undefined" is a just a fancy way of saying that there is no axiomatic system in place to calcualte this shit so I have no clue. And that is basically your answer.
You are dealing with meta-mathmatics not true mathmatics. It becomes a philisophical issue.
If you ask me maths has nothing to do with fucking reality anyway.
This could quickly delve into the loss of sanity. I suggest sticking some wrestling on and forgetting abut it.
while on the toilet i pondered a circle
can we humans define Pi down to a Planck length?
if so then wouldnt all subsequent digits be meaningless and as undefined as x/0?
if Pi loses its relevancy at such miniscule distances can we safely state that contiguous digits after the final relevant digit be zero?
Pi is irrational. If it wasn't then a circle at an eventual resolution would have to be made up of straight lines. This is not the case, of course. Meaning that Pi is basically irrational to infinity.
That's the mathmatics of it.
But for a circle drawn to a finite size its possible to specify a segment length where the segment is indistinguishable from a straight line. Thats Planck length. so the expression of the ratio of the circle's circumference to its diameter will have a limit to its consequential accuracy.
"Undefined" is a just a fancy way of saying that there is no axiomatic system in place to calcualte this shit so I have no clue. And that is basically your answer.
You are dealing with meta-mathmatics not true mathmatics. It becomes a philisophical issue.
If you ask me maths has nothing to do with fucking reality anyway.
This could quickly delve into the loss of sanity. I suggest sticking some wrestling on and forgetting abut it.