January 13th, 2016, 08:07 AM  #21 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,550 Thanks: 2551 Math Focus: Mainly analysis and algebra  You don't understand the notation. I have already explained it to you twice. The notation does not describe a process, it describes the terms. All the terms can be thought of as existing at once. But there is no infinity in the definition anyway. So your argument makes no sense.

January 13th, 2016, 08:11 AM  #22  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,550 Thanks: 2551 Math Focus: Mainly analysis and algebra  Quote:
But the important point is that the representation doesn't matter. A third is a third, however you write it down. You might as well claim that some emotions do not exist in English because the language does not have the ability to express it exactly. It's clearly nonsense. We get around the problem by using other ways to express ourselves, or by using combinations of words. Last edited by v8archie; January 13th, 2016 at 08:17 AM.  
January 13th, 2016, 08:13 AM  #23  
Member Joined: Oct 2014 From: UK Posts: 62 Thanks: 2  Quote:
People who have a problem with the notion of infinity cannot think of the terms all existing at once. This is the bit that makes no sense to us. There are so many problems with this idea it is difficult to know where to start. But for this 'infinitely many' idea to be a valid notion in mathematics it needs to be well understood. If it was well understood and properly defined, then it would be possible to describe a process to convert 1/3 into base 10. No such description is possible. Last edited by Karma Peny; January 13th, 2016 at 08:24 AM.  
January 13th, 2016, 08:20 AM  #24 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,550 Thanks: 2551 Math Focus: Mainly analysis and algebra 
So what if you can't write the number down. It doesn't mean that the construction doesn't exist. But again, it doesn't matter if it doesn't exist. It wouldn't stop the number existing.

January 13th, 2016, 09:50 AM  #25  
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,621 Thanks: 117  Quote:
Last edited by zylo; January 13th, 2016 at 10:03 AM.  
January 13th, 2016, 10:04 AM  #26 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,550 Thanks: 2551 Math Focus: Mainly analysis and algebra 
No it's not. The $\displaystyle m \gt M$ are all finite. Infinity isn't even a number.

January 13th, 2016, 10:10 AM  #27 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,621 Thanks: 117  
January 13th, 2016, 10:21 AM  #28  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,978 Thanks: 788 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
I really don't understand the point of this thread. The decimal representation of a real number is just that....a representation. Two points: 1) Nobody said you can actually write out the decimal "expansion" of a real number. 2) Nobody said the decimal representation of a real number is 1 to 1 with the real numbers. Apparently 0.9999.... is equivalent to 1. What's the problem here? Dan  
January 13th, 2016, 10:27 AM  #29 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,550 Thanks: 2551 Math Focus: Mainly analysis and algebra 
Do you not understand the difference between a set and a number? $m$ is a number drawn from the set of all integers greater than the number $M$. The definition states that it doesn't matter which number $m$ you draw from the infinite set of numbers greater than $M$, the inequality will continue to hold.

January 13th, 2016, 10:30 AM  #30  
Senior Member Joined: Jun 2015 From: England Posts: 891 Thanks: 269  Quote:
Consider the line leading from you to your nearest McDonald's. That line may be broken down into indefinitely smaller sections, as a theoretical process, but they must definitely all exist for you to traverse it to obtain your BigMac and Fries. Interestingly, most mathematicians are hung up on analysis to the extent they find synthesis difficult. Your problem seems to be the reverse one. Last edited by skipjack; February 29th, 2016 at 03:09 AM.  

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