Is this theory true?

Question

A few years ago my father told me about a theory that he learned in math. He said if you cut something in half, you could keep breaking it in half forever. No matter how small is it, it could be microscopic and you could still break it in half an infinity more times no matter how small it is. It will never turn into nothing or completely disappear. Im not talking about actually breaking something in half, im talking about the theory of it. I found this hard to believe. What does this mean?

He said if you break this in half. Whatever size it becomes, it could be broken in half again, and again, and so on forever?

Answer 1

That works until you get down to the size of one molecule. Then if you cut it in half it would not be the same substance.

Answer 2

This is one of the two views.  It is the classical view,

On the other hand, there is quantum theory that states that there is a smallest dimension, which is not divisible.

Mathematically, it is possible to perform the dividing into two parts for as long as you care to calculate it.  In reality, it is probably not possible.

So, essentially, yes; it is possible to go on forever.

Answer 3

Mathematically, you can divide a number in half an infinite number of times. 1/2, 1/4, 1/8, 1/16, etc... The number on the bottom can get infinitely large, meaning the number itself is infinitely small. Physically, eventually you get to an atom and are physically unable to divide it in half.

Answer 4

Atoms can be divided. Atoms into protons and neutrons. Those into quarks. Quarks into leptons. There is never nothing, look it up.

Answer 5

Good question. Your father is right. I'll try and give you an answer, but it won't be easy to understand (until you've had a few years of college-level maths). First, you should realize that there is a big difference between (a) being able to do something an "unbounded" number of times, and (b) actually doing something an infinite number of times.

An example for case (a) is easy! Start with the number 1. Divide by two to get 1/2. Again, you get a 1/4. No matter what fraction I give you, you can multiply the denominator by 2 and get a fraction half the size. You can go on forever doing this, and never get zero. This might be what your father meant.

Case (b) is more difficult. To actually do something "an infinite number of times", we need something like the concept of a limit in calculus. Unfortunately, if you divide any number of two an infinite number of times using this concept, you will get zero. So repeated division by two won't be an example anymore.

The solution is to turn to something like set theory, where we can start with a set which is "infinite" in size. For example, start with all numbers between 0 and 1. Half

these numbers are greater than or equal to 1/2, and half less than or equal. Break the set in half by throwing out all numbers above 1/2. Now, of the numbers that are left, half are greater than 1/4, and half less than 1/4. Throw away the numbers which are less than 1/4. Now repeat: half the remaining numbers are GREATER than 3/8, so throw these away. Now half the remaining numbers are LESS than 5/16, so throw these away. If you repeat this infinitely many times you will be left with exactly one number: the number 1/3, which has binary expansion 0.010101... . Actually, you can use any pattern: always throw away the GREATER half, and you will be left with the number zero. Other patterns give other numbers. The moral of the story is that if you throw away half the numbers infinitely many times, you will be left with exactly one number.

Sorry for the clumsy explanation.

Answer 6

Is it possible to break an atom in half? It's not possible for now, but I do believe we could. Well, does number stop? If it does, probably that piece of that thing would be gone. Does the space have an end...I'm not sure, but I do believe that it go on forever. Yes, I do believe in your dad theory.

BTW-I do believe that there is other cells working for the smaller cells and smaller cells and even smaller cells......

Answer 7

It's called Zeno's Paradox essentially. In theory it's true...in practice........no.

Interesting to think about tho.

:)