February 21st, 2018, 05:43 PM  #11  
Senior Member Joined: Aug 2012 Posts: 2,007 Thanks: 574 
Zylo wrote: Quote:
Quote:
Zylo did not say that "every real number uniquely determines a decimal." Because in fact that is false. The real number $\frac{1}{2}$ is represented by two distinct decimals, $.5$ and $.4999 \dots$ But Zylo didn't say that. He said that every decimal uniquely specifies a real number. And this is perfectly correct. Given any decimal expression, it uniquely defines some particular real number. The fact that there are sometimes two different expressions that define the same number, in no way invalidates that fact. In other words, the mapping from reals to decimals is not a function. But the mapping from decimals to reals is a function. When you put in a decimal you always get back the exact same real. This is a classic example of my thesis. Zylo makes a simple point, and @v8archie lets his Zylo derangement syndrome, or ZDS, cause him to make an elementary error of logic. Some people are just triggered by Zylo. Yet in this instance, as can be plainly seen, Zylo is absolutely correct; and one of his regular detractors throws an insult in lieu of taking a moment to think clearly. Nothing personal @v8, you just happened to supply a nice datapoint for my thesis today. Last edited by Maschke; February 21st, 2018 at 05:56 PM.  
February 21st, 2018, 05:55 PM  #12 
Senior Member Joined: May 2016 From: USA Posts: 1,126 Thanks: 468  
February 21st, 2018, 09:02 PM  #13 
Global Moderator Joined: Dec 2006 Posts: 19,525 Thanks: 1748 
The original wording was followed by "The sequence IS the real number", which suggests that zylo may not have intended the interpretation that's mathematically correct.

February 21st, 2018, 09:34 PM  #14  
Senior Member Joined: Aug 2012 Posts: 2,007 Thanks: 574  Quote:
And the sequence IS the real number. That's what real numbers are: the limits of sequences of rationals. Ok, equivalence classes of Cauchy sequences of rationals. But closer in spirit to what Zylo said, than with your interpretation of what you wish Zylo had said so that you could save v8archie's error. The sufferers of ZDS simply can't help themselves. This is why I love Zylo's posts. He shows how many people are reacting emotionally, when they should be working harder to understand the math themselves. People who should know better say strange things when in the grip of ZDS. Then they call for banning Zylo. Better they should spend their energy clarifying their own thoughts. If someone asks you, what are the real numbers, really; the correct answer is that morally, the real numbers are sequences of rationals. Everything else is technical details. A real number literally is the sequence of partial sums of a given decimal expression. Zylo has it right. Last edited by Maschke; February 21st, 2018 at 09:44 PM.  
February 21st, 2018, 10:08 PM  #15 
Global Moderator Joined: Dec 2006 Posts: 19,525 Thanks: 1748 
The literal meaning wouldn't have been changed if zylo had omitted the word "uniquely", and the next sentence used the wording "the sequence" rather than "a sequence". Bearing in mind that zylo once created a thread with the title "Decimal representation is unique", it's far from clear that this thread wasn't intended to take the same line.

February 21st, 2018, 10:36 PM  #16 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,638 Thanks: 570 Math Focus: Yet to find out.  I think this is the 'ZDS' Maschke is talking about. Bias and reputation carrying over from post to post. I have to say I like the efforts to preserve neutrality here.

February 21st, 2018, 11:21 PM  #17 
Global Moderator Joined: Dec 2006 Posts: 19,525 Thanks: 1748 
Let's wait for zylo to explain what he meant, and why he used the word "uniquely". I'd also like to know what zylo meant by "limits are defined properties of real numbers", as one can certainly have limits of imaginary numbers.

February 21st, 2018, 11:36 PM  #18  
Senior Member Joined: Jun 2015 From: England Posts: 853 Thanks: 258  Quote:
Quote:
One thing this shows is just how easy it is to develop circular arguments when considering this subject. Which came first the limit or the number?  
February 22nd, 2018, 02:40 AM  #19  
Math Team Joined: Dec 2013 From: Colombia Posts: 7,395 Thanks: 2476 Math Focus: Mainly analysis and algebra  Quote:
To draw an analogy: if your experience of someone is that they make up stories all the time, you are not likely to treat any new story they tell you as fact. I honestly interpreted the sentence as implying that the definition of each real number is unique, perhaps influenced by all Zylo's previous output. If that wasn't the meaning that he meant to communicate, I was in error. But I think it's an entirely reasonable interpretation in the light of the other stuff he writes.  
February 22nd, 2018, 03:45 AM  #20  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,888 Thanks: 765 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  

Tags 
limits, numbers, real 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Real Numbers and Natural Numbers  zylo  Topology  14  May 10th, 2017 01:57 AM 
Dimensions, and numbers beyond real numbers  Elektron  Math  4  May 7th, 2017 11:47 AM 
Real Analysis: Numerical Sequences (limits)  Luiz  Real Analysis  3  March 23rd, 2015 07:08 AM 
Real Analysis: Numerical Sequences (limits)  Luiz  Real Analysis  1  March 18th, 2015 08:39 AM 
Let a,b be real numbers such that....  thehurtlooker  Algebra  3  April 9th, 2013 12:58 AM 