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February 21st, 2018, 06:43 PM   #11
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Zylo wrote:

Quote:
 Originally Posted by zylo REAL NUMBERs are defined uniquely by "infinite" (unending) sequences of natural numbers. The sequence IS the real number.
And @v8archie replied:

Quote:
 Originally Posted by v8archie This, on the face of it, claims that $0.999\ldots \ne 1.000\ldots$. Presumably this is an extension of the usual failure to grasp the difference between "infinte" and "arbitrarily large". Do we really need another thread about that?
Now this is exactly the kind of post I was talking about earlier, where the attack on Mr. Z tells us more about the attacker than it does about Mr. Z.

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 06:56 PM.

February 21st, 2018, 06:55 PM   #12
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Quote:
 Originally Posted by zylo 0=.000000000...................................... ...
And your definition of the natural numbers includes 0?

 February 21st, 2018, 10:02 PM #13 Global Moderator   Joined: Dec 2006 Posts: 20,271 Thanks: 1959 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, 10:34 PM   #14
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Quote:
 Originally Posted by skipjack 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.
What Zylo said was correct. What v8archie said was wrong. The phrase "... which suggests that zylo may not have intended ..." is a symptom of ZDS. My point exactly. People just can't help themselves. I'm telling you, this fascinates the hell out of me.

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 10:44 PM.

 February 21st, 2018, 11:08 PM #15 Global Moderator   Joined: Dec 2006 Posts: 20,271 Thanks: 1959 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, 11:36 PM   #16
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Quote:
 Originally Posted by skipjack 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.
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 22nd, 2018, 12:21 AM #17 Global Moderator   Joined: Dec 2006 Posts: 20,271 Thanks: 1959 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. Thanks from topsquark and Joppy
February 22nd, 2018, 12:36 AM   #18
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Quote:
 Maschke That's what real numbers are: the limits of sequences of rationals
Quote:
 skipjack I'd also like to know what zylo meant by "limits are defined properties of real numbers",

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, 03:40 AM   #19
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Quote:
 Originally Posted by Joppy 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.
I don't think there's anything wrong with such a bias. It's entirely natural. Each thread does not occur within a vacuum.

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, 04:45 AM   #20
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Quote:
 Originally Posted by v8archie I don't think there's anything wrong with such a bias. It's entirely natural. Each thread does not occur within a vacuum. 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.
I agree. zylo has posted a number of threads "disproving" the Cantor diagonal argument. This topic has been featured in a number of his threads and as he doesn't seem to be able to understand that his argument is flawed I can easily see him post about it again in a new thread. I'm not trying to say that he will actually do so but is my suspicion based on bias or based on past experience?

-Dan

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