If you cut an object in half and half ... how far/small can you go ?

Answer 1

The answer is infinite. You can go forever. Every peace you have will have a half.It will never be zero.

As mathematically we can prove as:

Lim x/2 = infinite
x--inf

Answer 2

The ancient Greeks thought about this. They realized there had to be a limit as to how small we can cut up anything.

They called the smallest piece we can ever get "atomos," meaning "that which can no longer be divided."

This is how we got the word "atom."

Well, technically it is impossible to use a knife to cut so fine.

On the other hand, we now know there are sub-atomic particles (which of course, are smaller than atoms).

But your question really is, is there a limit or not? Answer is, yes there is. We are dealing with real, physical objects here. We are NOT talking philosophy. In philosophy we can do "thought experiments" and ask "what if." But in the real world, things have a minimum size, have a minimum amount of energy (which is not zero), and the universe has a maximum limited size, and limited amount of energy. In the real, physical world, everything has its limits.

In this real world, it is impossible to go smaller than a certain size. There is a limit. This is just the way the universe is. This is just the way "stuff" is. This is straight talk, no philosophy, no whatever pair of dcuks.

Answer 3

Atoms can be ionized until no electrons are bound to the nucleus. The pieces left now are the free electrons and the nucleus.

The electron cannot be split because the energy you would need to break it apart would be enough to generate lots of electron-positron pairs. It is considered a point particle in almost all models.

The nucleus could be split further (i.e., fission) but the resulting products may not be a clean split. If beta particles are emitted, the leftover nuclei will have a different ratio of protons to neutrons than before. In effect, the original substance has changed.

The nucleus contains protons and neutrons which are known to consist of quarks. However, we cannot extract these quarks, because like the electron, trying to break apart a proton or neutron results in creating proton-antiproton pairs. A free neutron can decay into a proton and an electron and an antineutrino. So we can never get past protons and electrons and neutrons.

Answer 4

Actually, the above posters are all incorrect. There IS a smallest possible unit of something.... not in mathematics, but physics has a definition for it.

The Planck length, is the unit of length approximately 1.6 × 10−35 metres or about 10-20 times the diameter of a proton. It is in the system of units known as Planck units. The Planck length is deemed "natural" because it can be defined from three fundamental physical constants: the speed of light, Planck's constant, and the gravitational constant.

The Planck LIMIT Length is roughly one thousand orders of magnitude smaller than this. Theoretically, at this point nothing can exist on a smaller scale - it is the smallest possible unit of length. Your question asks at what level something can no longer be divided - while retaining its characteristics, one molecule of the substance. While retaining its status as an element of some sort, an individual atom. While retaining status as matter, an electron. There are smaller quantum particles than this - but the eventual limit at which even abstractly nothing can be smaller is this length.

Answer 5

Technically you could go on forever. What you are inquiring about is what are known as Zeno's Paradoxes.

In its original form, it says that you can never get from one point to another. If you need to go from point A to B, you must go half that distance. Then you must go half that distance. Then half that distance and so on and so on, always going another half distance. Basically you will never reach point B.

The same logic works for your question. You could theoretically cut an object in half forever, never ending in how small it could be.

Answer 6

By cutting (mechanical process) you can only go down to the size of molecules. You can't go to atoms because you'll need to use a chemical process to break molecules. If you're cutting a piece of wood with a knive you'll never get carbon and oxygen separated. The first answer is almost correct, though it should have said "substance" not "matter".

Answer 7

You can divide it till an atom. thats the last case in which it has individual properties. dividing into neutrons protons and electrons after that loses its properties. you cant seperate the sub-sub-atomic particles called quarks as their property is that the force of attraction increases with distance. so go on! ruin your life pulling the chewing gum and bringing back again

Answer 8

you can cut something infinite small. Think opposite of the universe how its SO big its infinite splitting something is infinite too. however an atom is the small you could cut something while maintaining its natural substance.

Answer 9

The smallest piece of matter that can exist by itself is the molecule.