May 26th, 2017, 12:32 PM  #11 
Member Joined: May 2017 From: USA Posts: 31 Thanks: 0 
Thanks, but, no matter decimals or numbers above , they represent measurements and they are real and endless . Am I right?

May 26th, 2017, 01:00 PM  #12  
Senior Member Joined: Aug 2012 Posts: 2,306 Thanks: 706  Quote:
They could never represent measurements in the physical world. All physical measurement is approximate. A physical measurement is a value plus or minus a tolerance along with a probability curve saying how likely it is that the actual value is within tolerance. Physical measurements are nothing like mathematical real numbers, which are highly idealized. As far as being real, well the real numbers are anything but! The real numbers are a mathematical abstraction; and the more you learn about them, the more you realize how idealized and unphysical they are. And when you say endless, I pointed out that their decimal representation is infinite, but the numbers themselves are just numbers. $3$, $37$, $\pi$, $\sqrt{2}$ are all just real numbers. The word endless doesn't even apply. They each represent a particular point on the real number line. You wouldn't call a single point "endless," would you? It's just a dimensionless point. That's what a real number is. A point on the real number line. And the real number line doesn't exist! It's just a mathematical abstraction. Last edited by Maschke; May 26th, 2017 at 01:07 PM.  
May 26th, 2017, 01:39 PM  #13 
Member Joined: May 2017 From: USA Posts: 31 Thanks: 0 
Thanks and I still believe that they are real. There is no abstraction. If I have one full apple and I know I can make 0.5 of it, that means 0.1234512345... part of apple is real too, because its a part of one full apple, even knowing that I will not be able to see or touch it. From this view of point, one full apple is a combination of infinite infinity particles of it. 
May 26th, 2017, 01:46 PM  #14 
Member Joined: May 2017 From: USA Posts: 31 Thanks: 0 
Just like our universe has no starting and no ending point. Sorry, but it is a my theory that I can't get rid of it from my thinking. Thanks again.

May 26th, 2017, 02:44 PM  #15  
Senior Member Joined: Jun 2014 From: USA Posts: 525 Thanks: 40  Quote:
You can't divide an apple *exactly* in half in reality. Do you understand this, or is your theory that you can, in fact, divide apples into whatever real parts you want? If that is your theory, you will want to prove it. How would you prove it?  
May 26th, 2017, 04:42 PM  #16 
Member Joined: May 2017 From: USA Posts: 31 Thanks: 0 
In the first place, I would like to thank you all ! If I take interval 0 to 1, which has a starting point 0 and ending point 1. I will never pass through, into interval 1 to 2, by picking the particles that are endless in size like: 0.9 0.99 0.999 0.9999... and so on This is why I said  " infinity is always more than 0 and less than 1 ". 
May 26th, 2017, 05:04 PM  #17  
Senior Member Joined: Aug 2012 Posts: 2,306 Thanks: 706  Quote:
One big problem your theory has is that it contradicts known physics. Now that by itself is no proof that you are wrong. Einstein's work contradicted known physics too, and in the end he was right and known physics was wrong. That's science. However this DOES mean that the burden of proof is on you. Can you see that? The particular point of trouble is that you are claiming that actual infinity is instantiated in the universe. Contemporary physics does not support that idea. Last edited by Maschke; May 26th, 2017 at 05:12 PM.  
May 26th, 2017, 05:34 PM  #18 
Member Joined: Jan 2017 From: California Posts: 80 Thanks: 8 
I didnt know discussions like this were taking place in this forum. Wow this is deep... I can see what Microlab is thinking. could it be the reason why they say that some infinities are bigger than other infinities. I saw some guys talking about it on TV i was lost. 
May 26th, 2017, 05:38 PM  #19  
Senior Member Joined: Aug 2012 Posts: 2,306 Thanks: 706  Quote:
1) Math $\neq$ physics; and 2) The different levels of infinity are facts of mathematics and not physics. In fact the very existence of infinity in math is an arbitrary assumption called the axiom of infinity. What that says basically is that there is an infinite set! Infinity is just an assumption we use in math. Nobody claims it's physically meaningful. Not only that: If you instead DENY that there are any infinite sets, you get a perfectly consistent theory of math. It's just not as much fun as assuming there are infinite sets, so mathematicians assume the axiom of infinity and don't worry about it. It's only math. Not physics. If infinite sets have any meaning or instantiation in the physical world, it's for future physicists to discover. In contemporary physics the universe is finite. The factoid I always remember is that there are about $10^{80}$ hydrogen atoms in the universe. That's a pretty small number by mathematical standards. And it's definitely finite. Last edited by Maschke; May 26th, 2017 at 05:44 PM.  
May 26th, 2017, 05:44 PM  #20  
Senior Member Joined: Jun 2014 From: USA Posts: 525 Thanks: 40  Quote:
Cantor was the mathematician to establish that infinite sets may have different cardinalities. He did this by showing that no surjective function exists from the naturals onto the powerset of the naturals. On the other hand, it is fairly easy to construct a function that is surjective (or even bijective) from the real numbers onto the powerset of the natural numbers. We then say that the natural numbers are one type of infinity while the set of real numbers and the power set of natural numbers are a different type. You can read more about cardinal numbers here: https://en.wikipedia.org/wiki/Cardinal_number Consider Microlab's assertion that infinity is always more than 0 and less than 1. Think about the function...: $$f(x) = \frac{x}{1x}$$ ...over the domain [0, 1). This function bijects [0, 1) with [0, $\infty$), meaning there is a 1to1 correspondence between each element of [0,1) and each element of [0, $\infty$). Thus, the set of reals on the interval [0, 1) is the same 'size' as the set of reals on the interval [0, $\infty$). In mathematical terms, we do not say 'size' though in general, we say 'cardinality'. In fact, what I've done is prove that the cardinality of the set of reals on each of those intervals is equal. Last edited by AplanisTophet; May 26th, 2017 at 06:40 PM.  

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