One hallmark of a troll is that he lingers in threads that don’t really interest him. Don’t let the door, well, you know.
Beeruser:
Perhaps you’d care to explain what happens to the two significant places in 4 times .7…? How does …08 disappear? Explain this to me in a logical way without mystical reference to useful concepts about things that don’t exist, and I give you my word that I will change my mind on the spot and agree with you.
“It is lucky for rulers that men do not think.” — Adolf Hitler
No, you’ve mangled the first proof, because of your prejudice against infinities. As you admit above, it doesn’t even prove what you say it proves anymore.
But 0.0[n-1]1 is not the smallest number. Surely, 0.0[n]1 is smaller, isn’t it? And 0.0[n+1]1 is even smaller! Thus, there is no smallest number, and there is no largest number, in your scheme.
No. For reasons I explained above, that n would be undefined.
I greatly respect your logic abilities, and therefore make you the same offer I made Beeruser. What happens to the …08 in 4 times .7…? Make sense of it for me, and I will acquiesce.
“It is lucky for rulers that men do not think.” — Adolf Hitler
Well, the topic interested me, hence the thread did too, until it was clear that you weren’t interested in logic.
But I must admit your little hissy fit at me caused me to stick around a few posts longer, because it’s normal to check and see, when someone’s angry at you, whether it’s justified, or whether it was just them.
Having adequately answered that, it seemed worthwhile to make the general observation that you’re trolling. Now my work here is finished, thank God.
Cabbage, BeerUser, Spiritus, slythe, Tris, RM, et al, I leave you to continue the sham debate with the very real troll. Or not, as the case may be. Cabbage, thanks for including the very accurate and complete explication of the role of 1-1 correspondences in distinguishing one cardinality, especially those involving infinity, from another.
Well, where the 1s came from is very clear. They were digits of the products. But what happened to the …08 in your nth step? Those values were also digits of the products in every step but the last one.
“It is lucky for rulers that men do not think.” — Adolf Hitler
Libertarian:
The reason I so often ask you to define your term is that you so often do not. Shal we review the number of times I have asked you to define your use of the notation 9… ? Shall we count how many times you have done so?
You keep asking “weher does the 08 go”? The answer is, it goes to the end, and we never reach the end. Now, please answer me a couple of questions:
Divide 1 by 9. How many digits are in the result?
Postulate a field of arithmatic in which addition is not a closed operation. (is n is a real. n+1 is not a real). Give a mathematical derivation for the terminus.
This from a man who compares himself to Galileo and attempts to overturn the work of Cantor with undergraduate sophistry.
The best lack all conviction
The worst are full of passionate intensity.
*
I defined that at the beginning of each proof. Now, if you ask me a hundred times to define I have already defined, that doesn’t say anything about evasion, but about harrassment.
If you say the …08 goes to the end, then why do you drop the digits? Why is your notation not 3.1…08?
You mean to the right of the decimal? There are (1 / 0.0[n-1]1) digits.
What do you mean by “field of arithmetic”? Do you mean just a field? And do you mean addition is closed, rather than not closed? And the terminus of what? Do you mean terminus as in algorithm theory?
“It is lucky for rulers that men do not think.” — Adolf Hitler
Perhaps you do, others don’t. The concept of an infinite regression has been extremely fruitful–but there have been many prominent mathematicians who have objected to it. Their objections have been answered, one by one. The only objections left are pretty much ones of personal preference.
I went back through all the posts in this thread, and I could not find those reasons. I even searched for “undefined”. Could you give me the date of the post? Thanks.
Ah, a challenge.
OK, can you divide in your arithmetic? What is 3.1[n]/4?
But, if I’m interpreting what you’ve said above correctly, the left hand side is defined but the right hand side is not. So,
what is the answer? What is 3.1[n]/4?
Actually, it would help what’s left of the discussion if Lib defined the reals. The OP just says, “Universal Set: the set of real numbers.” In LibMath, they seem to have a different composition than in everyone else’s mathematics.
No, you did not. You said:
Definition: .9… = .9[n].
Now, if we accept the 9… notation as signifying an endless sequence of 9s, then this simply establishes a notation. But you deny that standard notation has meaning. therefore I ask you what meaning you give to the notation. You answer, “I already told you”. Your statement is inaccurate. This is not harrassment on my part; it is sheer avoidance on your part.
That begs the question. Supply a value for n or a mechanism to determine n.
The best lack all conviction
The worst are full of passionate intensity.
*
In finite arithmetic, the largest number, of course, is the muliplicative inverse of the smallest one. Thus, the largest number is 1 / 0.0[n-1]1. If we call that number A, then A + 1 is undefined. Which is as it should be. A + 1 does not equal A. It is simply as meaningless as A / 0.
I underlined the search term for your convenience.
Let me say first that I hope that you are sincere, and aren’t just making fun of me and presuming that I am a moron the way Firefly did. Again, I assure you that if you explain to me what happened to the 08 in 3.1111…, I am willing to see the error of my ways and change my mind.
To answer your question, 3.1[n]/4 is undefined even though 3.1[n] is defined. Just like 3 / 0 is undefined even though 3 is defined.
But where is this leading with respect to the missing two places of 4 times .7…?
“It is lucky for rulers that men do not think.” — Adolf Hitler
I’m going to hold off for a bit in the hopes that I’ve actually run into a man (or woman), RM Mentock, who might actually explain this to me, rather than taunt me about it.
“It is lucky for rulers that men do not think.” — Adolf Hitler
Consider the set N, the natural numbers: {1,2,3,…}. Is there a last number in the sequence, or can we keep adding 1 to the previous term, over and over without a conclusion?
Libertarian – I am trying to explain it to you. You, however, sem to instinctively be shying away from questions that will demonstrate your error.
Definition: .9… = .9[n].
makes no sense unless one side of the equation is well understood. Of course, the thrust of your argument is that n represents the largest possible integer. A natural response to that is: prove that there is a largest possible integer. You seem to be saying that you have done so, but in your definitions you have assumed the conclusion.
The best lack all conviction
The worst are full of passionate intensity.
*
If you’re leading me into another “if you knew as much math as I do” dance, I swear to you that I will never address another post to you, but if you are sincere about this, I’ll let bygones be bygones, and answer you.
I know the theories as well as you do. It’s just that I challenge them, whereas you don’t. Okay?
The last natural number is 10[n-1].
Spiritus:
I appreciate your attempts to help, but I don’t think the Socratic method is very helpful here. Simply tell me what happened to the two significant digits in 3.1…08. Please.
“It is lucky for rulers that men do not think.” — Adolf Hitler
Libertarian:
I have told you; you simply do not like the answer. Nothing has happened to them; the solution for 4 X .77777… is 3.1111…
There are no mysterious missing digits.
Now, why do you persist in not examining your own definitions? Your position thus far is eactly analogous to “10 is the largest number. Therefore 1/20 is the smallest number. .9 exists. .99 is undefined. I have proved this by my argument, in which n=1.”
The best lack all conviction
The worst are full of passionate intensity.
*
Does that mean 10, followed by n-1 zeroes, before the decimal point? (Want to be sure, before I get shot down for using your notation incorrectly.)
How do you know it’s the last natural number? On which of your axioms do you base this? Why can’t I add 1 to it, the way I can to any other natural number? (OK, that’s multiple questions in a sense, but it’s really one question in essence.)