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memester
 
Reply Thu 28 Jan, 2010 12:40 pm
@Emil,
Emil;123277 wrote:
It is ∞-∞=∞, not ∞-∞=0.
it seems that you must be able to say that infinity does not equal infinity. even if considered an indefinite number, it has a definite description, and so subtracting X from X does leave zero
 
Emil
 
Reply Thu 28 Jan, 2010 01:36 pm
@memester,
memester;123290 wrote:
it seems that you must be able to say that infinity does not equal infinity. even if considered an indefinite number, it has a definite description, and so subtracting X from X does leave zero


I have no clue what you are on about and it is irrelevant to this thread.
 
Deckard
 
Reply Thu 28 Jan, 2010 01:46 pm
@Emil,
Emil;123285 wrote:
That's right. You can create any number of scenarios for this point.


An infinite number of scenarios? What's the probability that I came up with that one? But maybe that brings us back around to the infinite monkey theorem.

Never mind the monkeys for a moment; imagine one infinitely huge sheet of paper with every possible combination of alpha numeric characters. What is the probability that somewhere on the sheet of paper you will find Newton's Principia in full. Well I said it was there so that probability is 1. What is the probability that you will find it on the infinite sheet?

This is a lot like Borges's Library of Babel which you will likely enjoy if you have not already. See
The Library of Babel

But The Library of Babylon is already finished while the monkeys are still working. What's the difference?

There is a difference between saying "The Principia is there" and "The Principia eventually will be there" but this difference isn't all that different from the difference between saying "The Principia is there" and "I will eventually find it". It is the difference between the readers of the already written and the writers of the not yet written.
 
memester
 
Reply Thu 28 Jan, 2010 01:49 pm
@Emil,
Emil;123302 wrote:
I have no clue what you are on about and it is irrelevant to this thread.
If you have no clue, how did you know it's irrelevant ?
If we say infinity equals "X", then since X-X= 0, infinity minus infinity equals zero.

If you say that infinity is not a number, then in your equations, you are mixing numbers with things that are not numbers, and yet the equation has an "equals" sign.

Isn't what you are saying something like this; apple plus 5 = apple ?

Since it is my own appreciation of infinity , or you own, that is being used in the equation, subtracting something from itself gives zero.

subtracting an unspecified amount from the same unspecified amount gives zero, no ?
 
Zetherin
 
Reply Thu 28 Jan, 2010 02:04 pm
@Deckard,
Emil wrote:
I already told you why. 1/∞=0. There are an infinite number of points. It will hit only one of them at random. The arrow will hit the target, that is stipulated in the thought example.

No matter the number of points, if it will hit one of them, isn't the probability that it will hit one of them... well, 1? It's going to hit a point, no matter the point.

Or is there some language ambiguity with "any single point"?

What am I missing?

Deckard wrote:

The probability of a random arrow hitting somewhere within a square mile on an infinite plane is also 0.


What does that even mean? We take a square mile, a quantifiable measurement, and apply it in relation to an infinite plane?
 
Deckard
 
Reply Thu 28 Jan, 2010 02:17 pm
@memester,
memester;123307 wrote:


If you say that infinity is not a number, then in your equations, you are mixing numbers with things that are not numbers, and yet the equation has an "equals" sign.


Infinity is clearly different from other quantities in that it is infinite, unbounded, not a finite quantity. Technically it is not a number. Why not call it a number? Well, here we enter into the realm of definition. For another example, in some systems X/0 = infinity by definition but in most commonly used system 1/0 is "undefined" whatever the heck that means. I don't think these definitions need to be dogmatic; it can be enlightening to consider alternatives but at some point they do need to be agreed upon for other ideas to be communicated.
 
Emil
 
Reply Thu 28 Jan, 2010 03:33 pm
@Zetherin,
Zetherin;123310 wrote:
No matter the number of points, if it will hit one of them, isn't the probability that it will hit one of them... well, 1? It's going to hit a point, no matter the point.

Or is there some language ambiguity with "any single point"?

What am I missing?


Any given particular point, not any point at all. But yes the probability of it hitting a point is 1. This was a premise in the argument. But the point is that if you choose some point at random. The probability that it will hit that point is 0 and it is not impossible. Hence, probability zero does not imply impossibility.

---------- Post added 01-28-2010 at 10:33 PM ----------

Deckard;123311 wrote:
Infinity is clearly different from other quantities in that it is infinite, unbounded, not a finite quantity. Technically it is not a number. Why not call it a number? Well, here we enter into the realm of definition. For another example, in some systems X/0 = infinity by definition but in most commonly used system 1/0 is "undefined" whatever the heck that means. I don't think these definitions need to be dogmatic; it can be enlightening to consider alternatives but at some point they do need to be agreed upon for other ideas to be communicated.


Undefined means that it doesn't mean anything.

---------- Post added 01-28-2010 at 10:38 PM ----------

memester;123307 wrote:
If you have no clue, how did you know it's irrelevant ?


You can know that things are irrelevant but not know what they mean.

Quote:
If we say infinity equals "X", then since X-X= 0, infinity minus infinity equals zero.


This is false for discourses dealing with infinities. (∀x∈R)(X-X=0) is true. But (∀x)(X-X=0) is false.

Quote:
If you say that infinity is not a number, then in your equations, you are mixing numbers with things that are not numbers, and yet the equation has an "equals" sign.

Isn't what you are saying something like this; apple plus 5 = apple ?


I'm not a mathematician. I don't know about this infinity is/is not a number issue.

Quote:
Since it is my own appreciation of infinity , or you own, that is being used in the equation, subtracting something from itself gives zero.

subtracting an unspecified amount from the same unspecified amount gives zero, no ?


Not if the unspecified amount can be infinities. See my two formalizations above.
 
Deckard
 
Reply Thu 28 Jan, 2010 04:21 pm
@Emil,
Emil;123324 wrote:

Undefined means that it doesn't mean anything.

Yeah but what does that mean?
 
Pepijn Sweep
 
Reply Thu 28 Jan, 2010 05:02 pm
@Emil,
Emil;122539 wrote:
"Pr(P)" just means the probability of P. ">" means above and "0" means zero. :p

So I was just talking about something that has a probability of happening that is more than zero. All such things will happen given infinite time. Is it possible for a toddler to type a sentence from your chosen work by accident? Yes. It is also more than logically possible, it has a non-zero probability. Is it likewise for all the following sentences? Yes. Is it also a nonzero probability that the toddler will type them in a row? Yes but extremely unlikely. However given infinite time all such unlikely events will happen.


Given infinite time, the toddler will grow up and leave your typewriter to explore the world!
 
Deckard
 
Reply Thu 28 Jan, 2010 05:06 pm
@Pepijn Sweep,
Pepijn Sweep;123345 wrote:
Given infinite time, the toddler will grow up and leave your typewriter to explore the world!


That's why we have to chain the toddler to the keyboard by saddling him with student loans, and instilling him with something called a "work ethic."
 
Pepijn Sweep
 
Reply Thu 28 Jan, 2010 05:29 pm
@Deckard,
What Hermes was hitting people on the head? I thought it was just symbolic for bying an intermediair of humans, gods and the underworld?

With a national debt of est $40-000 a person at birth US toddlers are surely restrained. Given infinite time he will read Karl Marx.
 
Deckard
 
Reply Thu 28 Jan, 2010 06:10 pm
@Pepijn Sweep,
Pepijn Sweep;123355 wrote:
What Hermes was hitting people on the head? I thought it was just symbolic for bying an intermediair of humans, gods and the underworld?


Hermes of course is connected with wisdom; that is a gift that he can both bestow and take away. That's a mildly esoteric, but I think fairly accepted interpretation of why Hermes is both the god of wisdom and the god of sleep. As it turns out, the staff is really more of a magic wand than the bludgeon I thought it was.

The staff of Hermes is much like the Greek herald's staff, which acts as a flag of truce on the battle field so messages can get through. This makes sense since Hermes, as you said, is also the messenger god.

Here's a quote from the Iliad about Hermes causing people to go to sleep (mentally) or to awake (mentally). I pulled the quote off this website where you can find other interesting quotes HERMES GOD OF : Greek mythology

Quote:
"He [Hermes] caught up the staff (rhabdos), with which he mazes the eyes of those mortals whose eyes he would maze, or wakes again the sleepers. Holding this in his hands, Kratus (strong) Argeiphontes winged his way onward." - Homer, Iliad 24.339
 
memester
 
Reply Thu 28 Jan, 2010 06:19 pm
@Emil,
Emil;123324 wrote:


Undefined means that it doesn't mean anything.

---------- Post added 01-28-2010 at 10:38 PM ----------


You can know that things are irrelevant but not know what they mean.



This is false for discourses dealing with infinities. (∀x∈R)(X-X=0) is true. But (∀x)(X-X=0) is false.

I suspected that it involves both being true, and I think possibly what you posted confirms that it depends on how you would like to view the question.
I'll have to check on how to read the code. Smile

Quote:
I have no clue what you are on about and it is irrelevant to this thread.


Quote:
You can know that things are irrelevant but not know what they mean.


When I admitted that I was deluded, I wasn't. You're wrong.
 
Emil
 
Reply Thu 28 Jan, 2010 06:59 pm
@memester,
memester;123363 wrote:
I suspected that it involves both being true, and I think possibly what you posted confirms that it depends on how you would like to view the question.
I'll have to check on how to read the code. Smile


Its set theory mixed with predicate logic.

(∀x∈R)(x-x=0) means for all x that are members of of the set of real numbers, x-x=0.


(∀x)(x-x=0) means for all x, x-x=0.


Sorry. I forgot to change our capital X's to non-capital x's.
 
memester
 
Reply Thu 28 Jan, 2010 11:40 pm
@Emil,
Emil;123372 wrote:
Its set theory mixed with predicate logic.

(∀x∈R)(x-x=0) means for all x that are members of of the set of real numbers, x-x=0.


(∀x)(x-x=0) means for all x, x-x=0.


Sorry. I forgot to change our capital X's to non-capital x's.
then I'm claiming that Infinity is a Real Number. :poke-eye:
 
Owen phil
 
Reply Fri 29 Jan, 2010 04:48 am
@Deckard,
Deckard;123311 wrote:
Infinity is clearly different from other quantities in that it is infinite, unbounded, not a finite quantity. Technically it is not a number. Why not call it a number? Well, here we enter into the realm of definition. For another example, in some systems X/0 = infinity by definition but in most commonly used system 1/0 is "undefined" whatever the heck that means. I don't think these definitions need to be dogmatic; it can be enlightening to consider alternatives but at some point they do need to be agreed upon for other ideas to be communicated.


1/0 is undefined means, if ~(y=0) then x/y =df (the z: y*z=x).
That is, this definition excludes the case of y=0.

If we define x/y =df (the z: y*z =x), then x/0 does not exist for all x.

x/0 is not unique, therefore it does not exist, even though it is defined.
 
Emil
 
Reply Fri 29 Jan, 2010 02:42 pm
@memester,
memester;123396 wrote:
then I'm claiming that Infinity is a Real Number. :poke-eye:


But it isn't AFAIK. See Wiki.
 
Deckard
 
Reply Fri 29 Jan, 2010 03:05 pm
@Owen phil,
Owen;123417 wrote:
1/0 is undefined means, if ~(y=0) then x/y =df (the z: y*z=x).
That is, this definition excludes the case of y=0.

If we define x/y =df (the z: y*z =x), then x/0 does not exist for all x.

x/0 is not unique, therefore it does not exist, even though it is defined.


What I find interesting is that it became necessary to define x/0 as "undefined" so to speak. I could make up a new symbol and scrawl it onto a piece of paper. "What's that?" someone asks. "Oh that, I haven't defined it yet, it's undefined." But the difference between this type of purely arbitrary and unnecessary presentation of an undefined symbol and the occurrence of the x/0 is that x/0 comes up as a matter of course. One runs into it often; for example any time a function has denominator consisting of a single variable. It just keeps popping up almost as if it is demanding some kind of definition. I mean every school boy and girl runs across this eventually and says: "Hey that's weird." I tend connect this weirdness with the weirdness of x/∞. Sometimes I want to restore symmetry to the mathematical universe and define x/0 = but that leads to other problems. So I accept its undefined status provisionally but every once in a while I still say, "Hey that's weird."

It's interesting that a lack of uniqueness can be used instead of 'undefined' at least in cases involving a variable (e.g. x/0). That improves my concept of what definition means in mathematics. Thanks for the post.
 
Arjuna
 
Reply Fri 29 Jan, 2010 04:01 pm
@Deckard,
Deckard;123527 wrote:
What I find interesting is that it became necessary to define x/0 as "undefined" so to speak. I could make up a new symbol and scrawl it onto a piece of paper. "What's that?" someone asks. "Oh that, I haven't defined it yet, it's undefined." But the difference between this type of purely arbitrary and unnecessary presentation of an undefined symbol and the occurrence of the x/0 is that x/0 comes up as a matter of course. One runs into it often; for example any time a function has denominator consisting of a single variable. It just keeps popping up almost as if it is demanding some kind of definition. I mean every school boy and girl runs across this eventually and says: "Hey that's weird." I tend connect this weirdness with the weirdness of x/∞. Sometimes I want to restore symmetry to the mathematical universe and define x/0 = but that leads to other problems. So I accept its undefined status provisionally but every once in a while I still say, "Hey that's weird."

It's interesting that a lack of uniqueness can be used instead of 'undefined' at least in cases involving a variable (e.g. x/0). That improves my concept of what definition means in mathematics. Thanks for the post.
I ran into it on a pop-quiz many moons ago. I looked around the room and everybody else was writing. I was sitting there staring at the paper. Turns out one of the variables had been described as infinite in the scenario when what was meant was "infinite for all practical purposes." Everybody else got that but me. I've never been a very practical-minded person. Beware taking things literally.

I like your idea of randomly creating undefined symbols. When I get off work I'm sometimes non-verbal from having talked all day long. Next time somebody asks me something when I'm in that state, I'll say... "sorry it's undefined." That should get me some brownie points for normalcy.

Speaking of stupidity... sometimes people just mean "abnormal" when they say stupid?
 
Pepijn Sweep
 
Reply Sat 30 Jan, 2010 04:12 am
@Arjuna,
In Dutch stupid and Mute have the same word for it. Creating new sybols or concepts like 0 and , raise only new problems. Old saying in Holland: to speak is worth silver, to be silent is worth gold.

Education helps only so much to make men less stupid. It all depends on the information presented. Noticing a Anglo-Saxon tradition by many of us, I question the neutrality of the arguments on this Forum.
 
 

 
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