thomaq

can actual infinites exist? or is the concept of infinity by definition always potential?

Darth Dane

Well, the number Pi is infinite, or it is as far as we know.






DD - Pi Spliff

thomaq

with Pi it is the number of digits that are potentially infinite. for instance, no one will ever see all the numbers of Pi.

Darth Dane

Yes, it is possible it is infinite, since we can't make the experiment forever we will never really know will we?




DD - Infinite Spliff

Defiant Heretic

We cannot know for certain that PI has an infinite number of digits, because we would need an infinite amount of time to demonstrate this. However, if the number of digits is not infinite, it would be possible to determine the final digit.

I cannot think of a material instance of infinity, however we can create an infinite loop using computer code. The following loop will continue for an infinite amount of time (assuming that no external factors, such as a loss of power, interrupt it).

while (1) {
  /* Any instructions in here will repeat themselves an infinite number of times. */
}

Wiploc

How about the number of points on a one inch line?

crc

Defiant Heretic

But what if there is a smallest possible particle, something which cannot be divided? Then you can't really count any measurement smaller than it, and so any measurement becomes finite.

If you're just talking mathematically, then yes, but a point is an abstract.

asdf

that's when we get into quantum physics... planck length, quanta of time, stuff i really don't understand =P

Big Spoon

Mathematically speaking, infinity and infinitesimals are limits, you would say
"x tends to infinity" but never "x=infinity".
The natural numbers, {1,2,3,...} (and arguably 0) are actually the sizes of the finite sets and using set theory it is possible to demonstrate, as Georg Cantor did, that there are infinite different sizes of infinity. It is conjectured that the size of the continuum (the "real line") is "Aleph 1", the second size of infinity after the natural numbers (Aleph Null) but this is all very abstract and doesn't relate to physical infinity.

Peter Kirby

Proof That PI is Irrational.

best,
Peter Kirby