Infinity (split from Paradox)

[1x0]

On 2018. 01. 27. at 8:44 AM, Strange said:

On the other hand, mathematics shows us that there are an infinite number of real numbers between 0 and 1 and between 1 and 2. These infinities are the same "size" (but larger than the infinite number of integers).

On 2018. 01. 27. at 5:16 AM, OroborosEmber said:

if this is true why we need any numbers beyond 0 and 1? Feels like different scaling of the natural numbers.

What would be the difference between the infinite numbers between 0 and 1 or the infinite numbers between 0 and 1 000  

Edited February 11, 2018 by 1x0

[Strange]

1 hour ago, 1x0 said:

if this is true why we need any numbers beyond 0 and 1?

For counting things. 

1 hour ago, 1x0 said:

What would be the difference between the infinite numbers between 0 and 1 or the infinite numbers between 0 and 1 000  

These are the same size infinities. 

This is larger than the infinite number of integers (infinitely larger, in fact). 

[1x0]

13 minutes ago, Strange said:

These are the same size infinities. 

This is larger than the infinite number of integers (infinitely larger, in fact). 

This two statement feels antinomic. If the first is true how do you mean the second? 

How something can anything be infinitely larger than something pointing towards infinity when we do not really know can infinity exist at all...

Edited February 11, 2018 by 1x0

[Strange]

The number of real (uncountable) numbers is infinite and infinitely larger than the infinite number of integer (countable) numbers. 

https://en.m.wikipedia.org/wiki/Georg_Cantor

[1x0]

1 hour ago, Strange said:

The number of real (uncountable) numbers is infinite and infinitely larger than the infinite number of integer (countable) numbers. 

https://en.m.wikipedia.org/wiki/Georg_Cantor

Interesting. Thanks for the link.

It is not easy to perceive this concept... Infinitely larger than infinity.....while there is no sign of general physical infinity. 

What makes real numbers uncountable? We can count them although we can not reach their limitations (if they have any)..

If we could give a natural number (1) to every point of spacetime and try to count how many points we have in the universe could we do that theoretically and could we count at the same speed or faster, than reality itself in its entirety is developing? 

Edited February 11, 2018 by 1x0

[Strange]

43 minutes ago, 1x0 said:

What makes real numbers uncountable?

The fact that you cannot make a one-to-one mapping from integers to reals; however close two reals are, there are always an infinite number of reals between them. 

What I like about this proof is that it is entirely based on logic (proper logic, not the crank logic of “it makes sense to me”) and is therefore irrefutable. 

53 minutes ago, 1x0 said:

If we could give a natural number (1) to every point of spacetime and try to count how many points we have in the universe could we do that theoretically

As far as we know, space is continuous so you could not do this. 

[1x0]

4 hours ago, Strange said:

As far as we know, space is continuous so you could not do this. 

I do not really see this as a reason, why not to be able to determine the units of measurement and execute the measurement. 

Edited February 11, 2018 by 1x0

[Strange]

1 hour ago, 1x0 said:

I do not really see this as a reason, why not to be able to determine the units of measurement and execute the measurement. 

OK, you can choose any units you like (millimetres or light years) and divide space up like that. But it doesn’t really mean anything. 

[1x0]

10 minutes ago, Strange said:

OK, you can choose any units you like (millimetres or light years) and divide space up like that. But it doesn’t really mean anything. 

How do you mean this? It makes anything measurable and by that perceivable for us. 

Could you make a second last infinitely long? How? 

Edited February 11, 2018 by 1x0

[Strange]

4 minutes ago, 1x0 said:

How do you mean this?

You can use an imaginary grid of any size to count points in space. Like graph paper; it can have lines every mm or cm or metre or km or ...

7 minutes ago, 1x0 said:

It makes anything measurable and by that perceivable for us. 

Well I suppose you can measure anything you can perceive. 

 

7 minutes ago, 1x0 said:

Could you make a second last infinitely long?

Of course not. 

[dimreepr]

6 minutes ago, 1x0 said:

Could you make a second stretch infinitely long? How? 

 

Microseconds, nanoseconds, picoseconds take your pick.

[Strange]

5 minutes ago, dimreepr said:

Microseconds, nanoseconds, picoseconds take your pick.

That doesn’t change the length of a second though. 

[dimreepr]

No, Plank is a pain in the arse when trying to describe infinity.

Or understanding it.