4

I'm not sure how to prove this as my professor has not shown any proofs involving real world objects, but I believe that it is finite since we know that there exists an integer k = the number of trees on earth. So we can call set B = {1, 2, 3, 4, ... ,k} and A = the set of all trees currently on earth. Then we can say $f:A \rightarrow B$ such that $f(n)=n$ is a bijection so they are in 1 to 1 correspondence so $|A| = |B|$ thus A is finite?

EDIT: Correction to my assumption: I assume since B is actually countably infinite then A is countably infinite?

ComputerScience1994
  • 103
  • 2
    Assume that every tree has a trunk at least one square millimeter in cross-section Compute the area of the earth's surface in square millimeters. That is a number greater than the number of trees on earth. – John Wayland Bales Jun 29 '16 at 04:32
  • 1
    What's the difference between set $A$ and set $B$? –  Jun 29 '16 at 04:35
  • 1
    I don't see how this is a mathematical question. Either there is a finite number of trees on earth or there isn't. It seems impossible for there to be an infinite number of anything "real" (i.e. not theoretical) which would seem to prove that the number of trees are finite--but this is an assumption that is impossible to be proved. – Jared Jun 29 '16 at 04:39
  • 1
    "...since we know that there exists an integer k = the number of trees on earth." You are assuming your conclusion. – treble Jun 29 '16 at 04:42

1 Answers1

2

Let G be the volume of the smallest atom, let EarthV be the volume of earth. Clearly the number of trees is at most EearthV/G. A tree cant be smaller than an atom and G and EarthV are both finite therefore the number of trees are finite.

shai horowitz
  • 2,086