can you cut something in half infinite times?

Answer 1

This is a great question. It points out just how feeble the concept of infinity really is.

In math, there is the old paradox that points out pretty much the same thing you asked. Assume you are a runner who has to run a kilometer (1,000 meter) in order to win all the money in the world. No time limit, you just have to to cross that 1,000 meters mark, take your time, and you become the wealthiest person in the world. A snap right? Wrong.

The catch...you have to run that 1,000 meters in half-distance sprints. On your first sprint, you must go exactly 500 meters; on your second, you must go exactly 250 meters; then 125 meters; then 62.5 meters; followed by 31.25 meters; then 15.625 meters ...7.8125 ...3.90625 ...1.953125 ... until you finally cross the 1,000 meter marker. Will you ever collect that unimaginable wealth?

Actually, no...in theory you will forever be running half-distance sprints, getting ever closer to the end, but never touching it. But in reality, the only way you can touch that finish line is by not "exactly" halving one or more of the sprint distances. In which case, you bust the rules and would be disqualified.

So, like the paradox, you cannot cut something in half infinite times, when that something is finite, like a 1,000 meter run.

Your question about infinity is good because it was infinity that in part pointed out some weaknesses in relativity. When taken down to the atomic scale of things, relativity comes up with infinity (a singularity) as one of its answers. That happens because relativity assumes a dimensionless (a zero value) point subparticle of mass-energy.

Zero divided into anything yields infinity (actually an indeterminant). But physicists cannot accept infinity in a finite universe; so they began to look around for some way to avoid the infinity answer. Lo and behold, string theory posits a one-dimensional vibrating string of one Plank length (1.6X10^-33 cm) long. No more zeros, no more singularities, and no more infinity.

To my finite mind, the fact that mathematics can result in something called infinity, but our observable universe does not allow infinity, points out a major flaw in our mathematics.

Answer 2

No. I think people are confusing the definition of infinity. You cannot cut something in half 'infinite' times (which in itself is a paradox)

You can however continue to cut something in half for an indefinite period of time.


To make this easy to understand, and why you cannot cut something 'infinite' times, you must understand that infinity is unbounded.

When you cut something in half, you are bounding the set by how fast you are cutting it. If it is bound it is not infinite...so because you cut it in half in the first place, it CANNOT be cut in half infinitely. lol

Weird eh.

Answer 3

Each time you cut something in half your fraction becomes smaller. One devided by infinity gives you zero.
So you can't cut something in half infinite times literaly and theoretically.

Answer 4

no, eventually u will run of of stuff to cut, oh btw try this: get a piece of paper and fold it exactly in half, u wont be able to do it more than 7 times

Answer 5

Theoretically.

Answer 6

no, because something will run out after so many cuts.

Answer 7

theoretically sure, but i wouldn't even begin to get started with it. way too much trouble

Answer 8

is your meaning is it about sleeping ? may be I cat do it during I get sleep

Answer 9

Yes. No such thing as "zero".

Answer 10

mathematically