
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 18th, 2018, 07:27 AM  #1 
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  Real Numbers are a Subset of the Rationals
The following table, which is countable (google), includes all pos rationals and reals. The reals are a subset of the rationals if you define: Real: m/100000........., all m Note: Left column and Top row are endless, \begin{matrix} &1 & 2 & 3 & 4 & . & . &. \\ 1 &\frac{1}{1} & \frac{1}{2} & \frac{1}{3} &\frac{1}{4} & . & . &. \\ 2 & \frac{2}{1} & \frac{2}{2} & \frac{2}{3} & \frac{2}{4} & .&. &. \\ 3 & \frac{3}{1}& \frac{3}{2} & \frac{3}{3} &\frac{3}{4} &. & . &. \\ 4 & \frac{4}{1} &\frac{4}{2} &\frac{4}{3} & \frac{4}{4} &. &. &. \\ . &. &. & . & . & . & . & .\\ .&. &. & . & . & . & . &. \\ . &. & . & . & .& . & . & . \end{matrix}\\ 0 assumed included. 
May 18th, 2018, 08:40 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,463 Thanks: 1340 
$\pi \in \mathbb{R}$ $\pi \not \in \mathbb{Q}$ $\therefore \mathbb{R} \not \subset \mathbb{Q}$ 
May 18th, 2018, 09:11 AM  #3  
Banned Camp Joined: Mar 2015 From: New Jersey Posts: 1,720 Thanks: 125  Quote:
$\displaystyle \pi$ $\displaystyle \equiv$ 3 "+ " 1415926....../1000000....... That's awkward and requires refinement: my original version was: The real numbers in [0,1] are a subset of the rational numbers in [0,1]. From table. Real numbers in [0,1] = m/1000......... , all m In that case, a real number is N.r which is still countable: N is a subset of the rationals and so is r.  
May 18th, 2018, 09:29 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551  Quote:
I doubt zylo will accept your proof. He simply assumes again that an infinite set has the same cardinality as any other infinite set. There is no doubt that he has described an infinite set that includes all rationals. In fact, it includes every possible decimal representation of every rational number. He still has not shown how he matches each real to one of these representations. Obviously, he will have no difficulty matching a unique rational to one of those representations. But he neglects to show that the irrationals match up with the remaining representations. Instead he implicitly relies on his assumption. Last edited by JeffM1; May 18th, 2018 at 09:32 AM.  
May 18th, 2018, 09:33 AM  #5  
Senior Member Joined: Sep 2015 From: USA Posts: 2,463 Thanks: 1340  Quote:
It's my opinion you just want attention. Have fun.  
May 18th, 2018, 09:41 AM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,663 Thanks: 2643 Math Focus: Mainly analysis and algebra 
I recommend closing this thread and stopping Zylo from creating more like it. I can't see any value at all in rehashing this nonsense again.


Tags 
numbers, rationals, real, subset 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
are the real numbers truly more infinite than the rationals  phillip1882  Number Theory  7  September 10th, 2017 02:29 PM 
How many subset requires to cover all numbers from set  santosingh  Advanced Statistics  1  May 16th, 2012 04:58 PM 
Probability of finite padic numbers within rationals  elim  Probability and Statistics  0  July 21st, 2010 02:03 PM 
Proof of a subset of integer numbers and linear combinations  uberbandgeek6  Number Theory  1  February 4th, 2010 06:27 AM 
example of a subset of real numbers with two accumulationpts  boxerdog246  Real Analysis  3  October 6th, 2008 10:35 AM 