there is infinte space between them. How can that be possible: having infinity within a finite structure?)
Ex. 1.1, 1.01, 1.001, 1.0001, 1.00001, 1.000001, 1.0000001, 1.00000001, ad infinitum.
Any thoughts?
(Just something I was mulling around in my head one sleepless night.)
2006-10-24 07:40:10 · 8 answers · asked by JaMoke 4 in Science & Mathematics ➔ Other - Science
This thought is called the Zeno's paradox. A turtle and a man going on a race. The turtle gets 100 miles handicap from the man. The answer is the man never catches up with the turtle ever. This has no solution in Mathematics.
2006-10-25 04:43:33 · answer #1 · answered by Mathew C 5 · 0⤊ 0⤋
I asked a teacher about this many years ago. This is the same question as how you can reach a destination if you keep halving the remaining distance in getting there. The answer is that the sum of an infinite number of infinately small numbers is still finite. If the solution is finite, it can be reached.
No, I can't give the mathmatical proof. I forgot that years ago.
2006-10-24 16:06:12 · answer #2 · answered by wires 7 · 0⤊ 0⤋
Cool! Someone else who can't turn their brain off at night and go to sleep, like me.
Numerically, you are correct; this could go on forever with no resolution because every number, no matter how small, can be divided. However, let's take a look at the reality.
Think of a traffic accident. If the theory held true, there would never be any collisions; the vehicles could just slow their speed proportional to their distances from one another and bingo -- no collision, since distance would continually be sliced into ever decreasing segments. Unfortunately, for this to happen, we would have to be able to manipulate time as well.
Great question; just my thoughts on the subject.
2006-10-24 07:48:11 · answer #3 · answered by Lonnie P 7 · 1⤊ 0⤋
Mind-boggling, isn't it? Just think of the space between those numbers you've constructed as being infinitely--or, better, "arbitrarily"--close. You can make them as close together as you want, meaning that there's always room for more. The bottom line is that infinities act very strangely, often in ways that are very difficult to conceptualize.
2006-10-24 07:45:35 · answer #4 · answered by DavidK93 7 · 1⤊ 0⤋
1 to 2 is finite only because we define it that way. They are the subset of all numbers that we call whole numbers, and the difference between them are whole numbers, as well, and so we call them finite.
2006-10-24 07:44:12 · answer #5 · answered by Wally M 4 · 0⤊ 0⤋
It just means that every division can be further divided.
2006-10-24 08:19:33 · answer #6 · answered by davidosterberg1 6 · 0⤊ 1⤋
cool
2006-10-24 07:52:18 · answer #7 · answered by askalotofquestionsmom 1 · 1⤊ 0⤋
what makes you think it is a finite structure? just curious. explain your query a little better please.
2006-10-24 07:45:31 · answer #8 · answered by pito16places 3 · 0⤊ 2⤋