infinte space in 10 ft?

Question

I heard a theory i dont know if its true or not just wanted to get an explanation from someone smart enough to figure it out
the theory said that if you measure a distance of lets just say 10ft then divide that in half you get 5ft and then continue dividing in half you can go forever 5=2 1/2=1 1/4 and so on
there is no shortage of numbers which they said means in essence there should be an infinte amount of space but if theres an infinite amount of space then how come i can measure out 10ft and walk from here to there its a pretty well known theory cant remember who came up with it.
could someone smart please explaine this in a way other than saying something like because its wrong or saying and i thought i was stupid

All of your answers your really helpful
Sorry but i can only pick one ; )

Answer 1

This is a very old, philosophical question. In theory, we can continue to divide any value by 1/2, and carry that out to infinity. However, mathematicians really don't much care for infinity, even infinitely small. So, they've come up with a clever way to show that repeatedly halving something actually converges on zero; not infinitely small.

Assume X(0) is the starting value at n = 0. Then after n = 1, we have X(1) = 1/2 X(0). After n = 2, we have X(2) = 1/2 X(1) = 1/2 1/2 X(0) = (1/2)^2 X(0)

By inference, we have X(n) = (1/2)^n X(0); so that, after n -> infinity, we have X(infinity) = (1/infinity) X(0) and, as everyone knows, anything divided by infinity is zero; so X(infinity) = 0 X(0) = 0. As I said earlier, dividing anything in half an infinite number of times converges on zero, not infinity.

Answer 2

Mathematically you can half something an infinite number of times.

Whether or not this applies to the physical universe is questionable, and it probably turns out that space is quantized so you get to a point where it makes no sense to half the space.

Things like this happen a lot when applying mathematics to the physical world. Most mathematical models are only applicable to the physical world over a certain range, and then things start behaving differently than the model predicts.

Answer 3

Mathematically, there are an infinite number of points, infinitely close together in any limited space. So the space is not infinite, only the number of points you can fit into it because a point has zero size.

Answer 4

This is true in theory only. Eventually the space would become so small that it would no longer be able to be divided in half.

Answer 5

Each time you travel half the distance, it takes half the amount of time.

If you're travelling at 10 feet per second :

The first 5 feet takes 0.5 seconds;
The next 2.5 feet takes 0.25 seconds;
The next 1.25 feet takes 0.125 seconds;
...and so on and so on and so on ...

You'll never get past 10 feet as long as no more than one second elapses ... but since time keeps on moving, one second comes and goes, you've travelled 10 feet, and you should keep on walking down to the corner store and get yourself a soda to celebrate your triumph over the Forces of Intertia.