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

That's right. You can create any number of scenarios for this point.

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

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.

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

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.

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?

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.

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 ?

Undefined means that it doesn't mean anything.

"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!

What Hermes was hitting people on the head? I thought it was just symbolic for bying an intermediair of humans, gods and the underworld?

"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

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

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

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.

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.

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.

then I'm claiming that Infinity is a Real Number. :poke-eye:

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.