Okay, so you really are stuck on Zeno's paradoxes.Obvious Leo wrote: If you can't follow this then all hope is lost. An apple takes a finite length of time to fall from the tree to the ground. This time interval can be measured with a clock. If time was infinitely divisible then it would take an infinite length of time for the apple to fall to the ground. Infinity means exactly what it appears to mean.
See if you can follow this (again even though I already explained it):
Let's take the total time for the fall to be "t". And we are gong to divide that by a chosen standard for infinity, namely:
infA ≡ [1+1+1+...] by definition
so now we can say that:
1/infA = 1/[1+1+1+...] ≡ 1 infinitesimal by definition
So now we can use normal arithmetic (because we declared a standard for infinity, "infA" and defined it)
We now know that:
infA * 1/infA = 1, and that
infA * t/infA = t
That says that an infinity of our infinitesimals adds up to "t"
"t" was a finite value. We multiplied an infinitesimal value times an infinite value and got a finite value because the two cancel each other's infinite property.
That is how calculus works, by adding an infinite count of an infinitesimal amount. That is why it has that "Σ" cap-sigma symbol there, an infinite sum of an infinitesimal amount. Despite using infinities, calculus quite often, and very provably yields finite values. Do you disagree?
