There is no such a thing as a next number. What do I mean by that? Let's use 1 as an example. 1 does not have a number that is next to it. You might think 2 is the next number, but 1.5 is actually in between them.

The next number becomes interesting. Suppose you a have a inch piece of wood. Now let's look at it's half-point. It's half-point is 0.5, what comes next? It should be whatever is next to it, but there is nothing next to it. No matter what other length comes after it, there will always be a smaller length before it.

Let me get more in-depth. Suppose, after the 0.5 point of the wood, the next length is 0.6. That means 0.6 came before 0.55. It can also mean that the length 0.55 does not exist.

59 minutes ago, Farid said:

There is no such a thing as a next number. What do I mean by that? Let's use 1 as an example. 1 does not have a number that is next to it. You might think 2 is the next number, but 1.5 is actually in between them.

The next number becomes interesting. Suppose you a have a inch piece of wood. Now let's look at it's half-point. It's half-point is 0.5, what comes next? It should be whatever is next to it, but there is nothing next to it. No matter what other length comes after it, there will always be a smaller length before it.

Let me get more in-depth. Suppose, after the 0.5 point of the wood, the next length is 0.6. That means 0.6 came before 0.55. It can also mean that the length 0.55 does not exist.

There are an infinite number of points. Between two points is not as interesting as how these things are organised.

Check out Cantor

1 hour ago, Farid said:

There is no such a thing as a next number. What do I mean by that? Let's use 1 as an example. 1 does not have a number that is next to it. You might think 2 is the next number, but 1.5 is actually in between them.

The next number becomes interesting. Suppose you a have a inch piece of wood. Now let's look at it's half-point. It's half-point is 0.5, what comes next? It should be whatever is next to it, but there is nothing next to it. No matter what other length comes after it, there will always be a smaller length before it.

Let me get more in-depth. Suppose, after the 0.5 point of the wood, the next length is 0.6. That means 0.6 came before 0.55. It can also mean that the length 0.55 does not exist.

First what does this mathematical nonsense have to do with Classical Physics ?

Mathematically the issue of a next number depends upon which number system you are referring to.

Also the Axiom of Choice guarantees a well ordering of most number systems.

What you are trying to explore is that numbers in some numbers systems have no nearest neighbour.

To study this you need to look at neighberhoods, completeness and density from a mathematical set point of view.

Edited Friday at 08:17 PM4 days by studiot

42 minutes ago, pinball1970 said:

Check out Cantor

OP seems like something related to Zeno paradoxes. Bertie Russell, based on Cantor, offered a solution known as the "at-at theory of motion". It has problems too.

As @studiot pointed out, (1): This is not classical physics. And (2): "nextness" depends on the number system. There is a next number in the naturals, the integers, all the finite arithmetics, etc. There isn't in the reals or the rationals.

The question of whether there is a "next point" in physical space is equivalent to whether space is discrete.

Is that what you mean, @Farid ?

4 hours ago, Farid said:

There is no such a thing as a next number. What do I mean by that? Let's use 1 as an example. 1 does not have a number that is next to it. You might think 2 is the next number, but 1.5 is actually in between them.

The next number becomes interesting. Suppose you a have a inch piece of wood. Now let's look at it's half-point. It's half-point is 0.5, what comes next? It should be whatever is next to it, but there is nothing next to it. No matter what other length comes after it, there will always be a smaller length before it.

Let me get more in-depth. Suppose, after the 0.5 point of the wood, the next length is 0.6. That means 0.6 came before 0.55. It can also mean that the length 0.55 does not exist.

Quantization exists in physics.

Just like in computers.

You have a floating point number:

float x = 0;

and

float x = 1;

What is between them?

Many intermediates.

But you don't know how many there are unless you've read the IEEE 754 specification (and most people haven't).

https://en.wikipedia.org/wiki/IEEE_754

When you dig long enough, you achieve granularity, quantization, experimentally.

In physics, as you mentioned in relation to a piece of wood, it is made up of atoms, and by dividing it long enough, you achieve the graininess created by atoms. The length of a piece of wood can be given in the number of atoms in a straight line.

Your problem can be rephrased in simple terms: does the quantization of space and time exist?

Which is the problem I referred to with Russell. Physical spacetime is expected to be quantized because physical coordinates are slightly noncommutative, right?

Moderator Note

Moved to speculations

good explanation @studiot
The OP must be new to number and set theory.

As for the Physical points made by other members, although all other interactions are quantized, IOW discrete granularity, the space-time field of gravity may or may not, be granular/quantizable ( it certainly is not by standard perturbative methods ).