# Can be that the Natural Numbers are Finite?

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57 minutes ago, Conscious Energy said:

You can not have more natural number then the information about them in Nature. I think the present Time = Now provides a limit to information available.

Why not?

How much information is in the natural numbers? You need to rigorously quantify these things, rather than assert them.

52 minutes ago, Country Boy said:

The problem is that you say  you are talking about mathematics but you are actually talking about physics. You do not know what mathematics is and you do not know what physics is!  There is "infinity" in mathematics but there is no "infinity" in physics.

There are lots of infinities in physics, but they are described by math

38 minutes ago, Conscious Energy said:

Yes.
0 1 2 3 4 5 ….

the ones in Nature I can count with.

How many solutions are there for the principle quantum number for the Hydrogen atom (Schrödinger or Bohr solution; pick whichever one you want)

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On 9/29/2021 at 6:14 PM, swansont said:

You have an infinite number of points in any finite, one-dimensional line segment. So this is incorrect.

It should be pointed out that this is an uncountabe infinity. It is waaaaaaaaaaaaaaay bigger than the infinite cardinality of the natural numbers

Infinities come in different sizes

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Posted (edited)
1 hour ago, ydoaPs said:

Infinities come in different sizes

I have difficulties to imagine that a 1cm3 space can contain more points that the whole universe has all together.

I do not see how physically the whole Universe with all its distance could fit in 1 cm3 if it would be true.

Which law says a point has absolutely no space and a minimal length? How is it reasoned that a point of space has no physical extent?

I can count distance and time with the natural numbers.

Every point of space has a current moment of now.

I think a point has a minimal extent since it has a local space of recognition by the local time of observation. Even it is the smallest physically recognisable Space by the shortest moment of Time. Some space will be there. If not and a point has absolutely no space by the time of observation why and how that is possible?

Edited by Conscious Energy
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58 minutes ago, ydoaPs said:

It should be pointed out that this is an uncountabe infinity. It is waaaaaaaaaaaaaaay bigger than the infinite cardinality of the natural numbers

Infinities come in different sizes

I agree with both you and swansont, however I was holding off infinity until we had determined other definitions since CE is mixing up physics and maths, as several people have now commented.

It should also be pointed out that there is more than one type of infinity (or meaning to the word) which makes things more complicated.

I have already pointed out the easier question that we need CE's definition of natural numbers.

So thank you for this @Conscious Energy

3 hours ago, Conscious Energy said:

Yes.
0 1 2 3 4 5 ….

the ones in Nature I can count with.

OK so you wish to include 0 in the natural numbers. That is fine. Some Mathematicians include zero some do not.
Personally I prefer to start at 1 because it makes the philosophy of numbers easier and more elegant.

Either way we can state the following axioms to obtain all the natural numbers.

1) 0 is the first number.

2) Every number has a successor number, obtained by incrementing that number by 1.

It follows from these two axioms that 0 is the smallest natural number but there is no largest natural number.

This leads directly on to one type of infinity as a non terminating process.

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18 minutes ago, Conscious Energy said:

Which law says a point has absolutely no space and a minimal length? How is it reasoned that a point of space has no physical extent?

It's how they are defined.

If you had point with a finite length, you can make a point that's half the size. If you have endpoints a fine distance apart, you can choose a point between them. Keep doing so. The limiting case is that points have zero length.

18 minutes ago, Conscious Energy said:

I can count distance and time with the natural numbers.

You aren't counting points when you do this.

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15 minutes ago, Conscious Energy said:

I have difficulties to imagine that a 1cm3 space can contain more points that the whole universe has all together.

I do not see how physically the whole Universe with all its distance could fit in 1 cm3 if it would be true.

Which law says a point has absolutely no space and a minimal length? How is it reasoned that a point of space has no extent?

The first two lines are not true.

I recently quoted Euclid axioms which state exactly the last line to someone.

Was that someone yourself ?

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21 minutes ago, Conscious Energy said:

I have difficulties to imagine that a 1cm3 space can contain more points that the whole universe has all together.

Nobody has claimed this to be true.

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Posted (edited)
1 hour ago, studiot said:

Some Mathematicians include zero some do not.

Zero being a natural number, has nothing to do with that, some include it and some do not.

If the information is perceivable in the natural physical reality than it’s part of the natural numbers.

As far as I am able to perceive, in every point of space I can take 0 at any time.

I think the physical value of 0 is distributed by SpaceTime ( the physical 4D empty set).

Can a physically 0 entity (point of space) have minimal level of extent?

Edited by Conscious Energy
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2 minutes ago, Conscious Energy said:

Zero being a natural number, has nothing to do with that, some include it and some do not.

If the information is perceivable in the natural physical reality than it’s part of the natural numbers.

As far as I am able to perceive, in every point of space I can take 0 at any time.

I think the physical value of 0 is distributed by SpaceTime ( the physical 4D empty set).

Can a physically 0 entity (point of space) have minimal level of extent?

I thank you for responding to one thing I said, but I am sorry that you simple demonstrated that you don't know what you are talking about.

If you want more explanation all you had to do was ask.

Instead you chose, yet again, to challenge an attempt to help with nonsense.

Quote

As far as I am able to perceive, in every point of space I can take 0 at any time.

How can a point in space be counted a zero ?

This means that if I label a point 'zero' and I am counting points that I have no points

ie you are saying a point is not a point !

I am becoming weary of putting time and effort into this to no apparent purpose.

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8 hours ago, Conscious Energy said:

How can you have more (infinite) numbers than the information the universe provides?

My personal (and rather naive) answer:
We do not know if the universe* is infinite or finite and if there are infinite or finite number of particles.
Mathematics contain tools and concepts usable for both cases.

*) The observable universe is finite and contains a finite amount of matter.

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1 hour ago, studiot said:

I thank you for responding to one thing I said, but I am sorry that you simple demonstrated that you don't know what you are talking about.

If you want more explanation all you had to do was ask.

Instead you chose, yet again, to challenge an attempt to help with nonsense.

!

Moderator Note

Which seems to be a recurring theme with this poster, as well as his former account (good catch, swansont). Trolling their incredulity, belaboring the point, and obfuscating replies to reasoned arguments is the MO, which makes it difficult to discuss and impossible to learn. If you think there's anything meaningful to talk about here, I can leave the thread open, otherwise I'll shut it down.

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13 minutes ago, Phi for All said:
!

Moderator Note

Which seems to be a recurring theme with this poster, as well as his former account (good catch, swansont). Trolling their incredulity, belaboring the point, and obfuscating replies to reasoned arguments is the MO, which makes it difficult to discuss and impossible to learn. If you think there's anything meaningful to talk about here, I can leave the thread open, otherwise I'll shut it down.

Hopefully the trash can is not quite full yet.

I would recommend anyone who would like further informatuion to start their own thread, rather than try to disentangle this one.

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