View Full Version : 0% probability == impossible?

Silvercord

08-29-2003, 01:11 PM

if something has 0% probability does that mean it is impossible?

I dont' think it does, but, well, umm, yeah

anyway my math teacher says that is the probability of selecting an odd number on an infinite pascal's triangle

Thantos

08-29-2003, 01:37 PM

Probility is just how likely something is to occur. So 0 probility doesn't really mean impossible, just snowball chance in hell.

Silvercord

08-29-2003, 02:04 PM

ha, I like that, I'll have to use that one sometime.

that really makes sense that the probability is 0, because as the number of rows increase the probability of choosing an odd decreases, so 'at' infinity the probability 'is' 0.

confuted

08-29-2003, 02:07 PM

Yeah, one of the calculus rules is that

lim a/x = 0

x->infinity

where -infinity<a<infinity

Sang-drax

08-29-2003, 02:46 PM

Originally posted by Thantos

Probility is just how likely something is to occur. So 0 probility doesn't really mean impossible, just snowball chance in hell.

No, zero probability of success means that it is impossible.

confuted

08-29-2003, 03:11 PM

Technically... a 1/infinity chance...

But supposing that you have an infinite list (infiniteth row of pascal's triangle) with four odd numbers... You're not going to get an odd number.

Perspective

08-29-2003, 03:48 PM

Originally posted by Thantos

Probility is just how likely something is to occur. So 0 probility doesn't really mean impossible, just snowball chance in hell.

As sang-drax mentioned, 0 probability does mean its impossible. The actual probability of selecting a negative number is not equal to 0, rather it approaches 0 as the number of rows approaches infinity.

prob -> 0 as rows -> infinity.

Thantos

08-29-2003, 04:06 PM

Considering that you can never reach an infinate value, there will always be a chance to select an odd number. Since as you pointed out that the true probility will never actually reach zero there must be a chance for a condition to exist.

But supposing that you have an infinite list (infiniteth row of pascal's triangle) with four odd numbers... You're not going to get an odd number

I agree that a person won't get those odd numbers but it doesn't make it impossible.

Perspective

08-29-2003, 05:19 PM

>>

I agree that a person won't get those odd numbers but it doesn't make it impossible.

<<

no, its not impossible because the probability of getting an odd number is not 0, its approaching 0.

In general, saying something has 0 probability is saying that it can not and will not ever happen. The reason that it is not impossible to get odd numbers is because the probability of getting an odd number is not actually 0, it is approaching 0.

goran

08-29-2003, 09:57 PM

I left mathematics long back but could not resist a dig at this. Infinity cannot be defined. So, I second Perspective when he says

its not impossible because the probability of getting an odd number is not 0, its approaching 0.

Jeremy G

08-29-2003, 10:13 PM

0% probability BY DEFINITION DICTATES that it is an impossible event.

Thantos

08-29-2003, 10:26 PM

Originally posted by dbgt goten

0% probability BY DEFINITION DICTATES that it is an impossible event.

Just because mathmatations define it to be impossible does that truely make it so? For all tense and purposes it is impossible, doesn't mean its really true.

Silvercord

08-29-2003, 11:54 PM

goten and perspective and everyone else is right, it is impossible. we're not just talking about a large number of rows, we're talking about an infinite number of rows. Perspective summed it up nicely, as the number of rows increase, the probability of getting an odd decreases, therefore when you are at inifinity it is 0. end of discussion. let's go disco

Magos

08-30-2003, 03:50 AM

Isn't "impossible" defined as "posibility = 0"? I mean, everything but 0 is posible so what's left (0) must be impossible...

*ClownPimp*

08-30-2003, 10:38 AM

>anyway my math teacher says that is the probability of selecting an odd number on an infinite pascal's triangle

The fact that the triangle is assumed to have an infinite number of rows means that the probability *is* 0 (not approaching zero). Infinity is a concept. While it is true no one can never enumerate infinity, the concept is still valid. Thats why calculus was invented, to define the concepts of infinites and infintesimals and to be able to do math with them.

Perspective

08-30-2003, 11:04 AM

>>

The fact that the triangle is assumed to have an infinite number of rows

...

While it is true no one can never enumerate infinity,

<<

Contradiction.

if the triangle has an infinite number of rows then you have just enumerated infinity my friend. The triangle will always have a discrete countable number of rows. Thas why in calculus we say as <stuff> approaches infinity and not when <stuff> equals infinity.

Zach L.

08-30-2003, 11:25 AM

Right, the problem is that we a dynamicaly changing quantity (as Perspective said, "approaching") is being treated as a static quantity. The concept of infinity is valid, but nothing can "be at" or "reach" infinity, so we have to define the behavior as what happens as our quantity grows without bound.

kermit

08-30-2003, 11:38 AM

Originally posted by Zach L.

...but nothing can "be at" or "reach" infinity,...

Nothing finite that is. Its hard to think of the immaterial as being "something."

Zach L.

08-30-2003, 04:39 PM

Touché. More properly phrased, a quantifiable property such as the number of rows cannot 'equal' infinity, but can 'tend towards' infinity. :)

*ClownPimp*

08-30-2003, 05:00 PM

>if the triangle has an infinite number of rows then you have just enumerated infinity my friend. The triangle will always have a discrete countable number of rows

your not thinking abstractly. It is true that in real life, youll never find a pascal triangle with an infinite number of rows. But that is besides the point. One can consider a pascal's triangle with an infinite number of rows. And when one does that, it will have a probability of zero of selecting an odd number.

And anyways, were not talking about a 'real' triangle, so there is no law that says every side has to have a discreet length. So there is no contradiction, my friend.

Zach L.

08-30-2003, 05:30 PM

He is thinking abstractly. You have a contradiction in your statement: "oull never find a pascal triangle with an infinite number of rows." Quite true. Infinity is not a number. And if we just consider a generic 'triangle' whose sides are infinitely long, we can make no conclusions about its properties. If we consider a finite triangle, and place no bounds on its side-lengths, then we can analyze its properties, and discover trends as the side-length grows without bound.

*ClownPimp*

08-30-2003, 05:46 PM

>He is thinking abstractly. You have a contradiction in your statement: "oull never find a pascal triangle with an infinite number of rows."

I fail to see any contradiction in my statements, and you have yet to point any out. Remeber, my complete statments was "In real life, youll never find a pascals triangle with an infinite number of rows". I am speaking conceptually when I say to consider a pascals triangle with infinite rows.

Perspective

08-30-2003, 06:49 PM

>> consider a pascals triangle with infinite rows

i understand what you are trying to say but your wording provides the contradiction i mentioned above. The triangle does not have an infinite amount of rows, rather, the number of rows it has approaches infinity.

confuted

08-30-2003, 07:13 PM

Originally posted by Perspective

>> consider a pascals triangle with infinite rows

i understand what you are trying to say but your wording provides the contradiction i mentioned above. The triangle does not have an infinite amount of rows, rather, the number of rows it has approaches infinity.

Agreed. Let x denote the number of rows. Let y denote the number of terms in a row. For the first few values of X:

x|y

---

1|1

2|3

3|5

4|7

It's obviously a linear relationship, with the equation y=2x-1. Now, for a bit of calculus...

lim y=2x-1 = infinity

x->infinity

However, if you know calculus, you'll know that what I just wrote is read like this: "the limit of y equals 2x minus 1 as x approaches infinity is infinity." Infinity is not an integer, guys. It's not even a number. It's a concept. For any countable number of rows x, the probability of picking an odd number is inversely proportional to x. I think I said that correctly. Anyway, suffice it to say that if you HAVE a certain row X, meaning that it actually exists, the probability of picking an odd number can be computed and will not be zero, although it may be close. The probability approaches zero as X approaches infinity, but if you are given a row X, it is not the infiniteth row.

</rant>

Unless you understand the concept of limits, just read that and accept it. Then take a calculus class ;)

*ClownPimp*

08-30-2003, 07:14 PM

There is no contradiction in my statement.

>if the triangle has an infinite number of rows then you have just enumerated infinity my friend. The triangle will always have a discrete countable number of rows.

We are assuming the triangle has an infinite number of rows. Therefore, by the definition of infinite, the triangle cannot have a discrete countable number of rows.

Also, there is nothing in the definition of pascals triange that requires the triangle to have a discrete countable number of rows, so assuming that the number of rows is infinite doesnt lead to a contradiction.

*ClownPimp*

08-30-2003, 07:19 PM

>However, if you know calculus, you'll know that what I just wrote is read like this: "the limit of y equals 2x minus 1 as x approaches infinity is infinity."

Again, the problem assumed the triangle had an infinite number of rows, am I the only one who seems to get that?

confuted

08-30-2003, 07:27 PM

You're the only one that doesn't quite get it :P If you are given a row and told that it is the "infiniteth row," then surely it isn't. Anyway, we've answered the original question by now...

*ClownPimp*

08-30-2003, 08:04 PM

>If you are given a row and told that it is the "infiniteth row," then surely it isn't.

What?

confuted

08-30-2003, 09:10 PM

infinity can not be enumerated. You can not have the infiniteth something.

*ClownPimp*

08-30-2003, 10:00 PM

>infinity can not be enumerated. You can not have the infiniteth something.

I agree. But how does that contradict what i stated?

Zach L.

08-30-2003, 11:07 PM

You cannot have any 'infinite number' of rows. There lies the contradiction. There is no such thing as an 'infinite number'. Numbers are finite, but not necessarily bounded. As I said earlier, given an 'infinite triangle', you cannot say anything about its properties. Given a finite triangle though, you can determine its properties (ie, the probability of picking an odd), and then determine the trend of those properties as its size grows without bound.

Sebastiani

08-31-2003, 12:39 AM

This is a perfect example of how mathematics breeds insanity.

Infinity-approaching rows and zero-probabilities are mere fictions of the feeble human mind. Rows will always be finite and nothing is totally impossible. See? No math necessary.

Clyde

08-31-2003, 02:13 AM

You cannot have any 'infinite number' of rows. There lies the contradiction. There is no such thing as an 'infinite number'

I can construct a fractal (conceptually) based on mathamatical rules, it is even fairly tangible, what is its length?

- But i think you are arguing over semantics, i think its fair to say you can make statements about infinite triangles, it's just that those statements are based on extrapolations from finite ones.

Rows will always be finite and nothing is totally impossible

Plenty is totally impossible.

*ClownPimp*

08-31-2003, 06:44 AM

Everyone keeps saying how you cant have an infinite number of rows. But what you dont seem to get is that there is nothing inherently flawed about the assumption that your pascals triangle does. If there is point it out to me. Dont just say "you cant have that".

>You cannot have any 'infinite number' of rows. There lies the contradiction. There is no such thing as an 'infinite number'. Numbers are finite, but not necessarily bounded

When i say infinite number of rows, I mean the number of rows cant be counted. Let me define what I mean by infinite number of rows.

Let N be the number of rows in the pascals triangle. For all n in Z > 0, N > n.

this is a bad definition, since it assumes the number of rows can be counted, here is a better one

For all n in Z > 0, there exists N in Z such that N > n and there is an Nth row in the pascals triangle (where Z is the set of integers)

What that means is that for any number you choose, there is a number greater than that in which the pascals triangle has a row with that number. There is no contradiction in that, therefore there is no contradiction in me assuming the pascals triangle has an infinite number of rows.

Futhermore, there is a branch of mathematics where the number line has infinity on the ends, basically as an actual number. I dont remember what it is called since our calc teacher just briefly touched on it. So the idea of something being infinite isnt completely foriegn in mathematics.

[edit]

>But i think you are arguing over semantics,

Im starting to think so too.

Sang-drax

08-31-2003, 07:08 AM

If you have an area with a point in it and you select another point at random, the probability that you would select the original point is zero.

Why? Because the area has an infininte number of points.

Clyde

08-31-2003, 09:33 AM

Futhermore, there is a branch of mathematics where the number line has infinity on the ends, basically as an actual number. I dont remember what it is called since our calc teacher just briefly touched on it. So the idea of something being infinite isnt completely foriegn in mathematics

I don't like that because you can have two infinitely large (or small) 'numbers' and one can be bigger than the other.

Clyde

08-31-2003, 09:36 AM

If you have an area with a point in it and you select another point at random, the probability that you would select the original point is zero.

Why? Because the area has an infininte number of points

I don't think thats right, you merely have an infinitely small chance of selecting the original one.

If you repeated the selection an infinite number of times you could end up selecting the same coordinates.

If the the probability was really zero repeating it an infinite number of times would make no difference. You could never select it again.

Zach L.

08-31-2003, 10:21 AM

Even in that example, you don't can't say "I have infinite points, and therefore..." You can say, "The chance of choosing the original point is inversely proportional to the number of points, so as the number of points grows without bound (tends toward infinity/<insert your choice of wording>) the probability goes asymptotically toward 0." Infinity is not in any set of numbers, so the operation '1/infinity' is not closed for any set. One can see however, that the behavior is for the value to go to 0.

Clyde, the fractal of course, is said to have infinite length (I can think of a few such examples). The thing is, even that is a limiting process. Take Sierpinski's triangle, you start by cutting the inscribed equilateral triangles out. You start with both finite perimeter, and a non-zero zrea. As the number of repetitions of this cutting process grows without bounds though, so does the perimeter, and the area trends toward 0.

*edit*

The problem with having an 'infinite number' of anything is that the term 'number' implies that the actual amount belongs to some set of numbers (Z, Q, R, C, ...). Each element of these sets are finite, however. Interestingly enough, the sets themselves are unbounded (have infinitely many elements, if you will), though they are different orders of infinity.

Perspective

08-31-2003, 11:40 AM

>> point it out to me

your triangle has an infinite number of rows. let 'n' denote the number of rows in your triangle.

now i'll define a new triangle with n+1 rows. my new triangle has more rows than yours yet yours has an infinite number of rows. obviously this is wrong.

That is why you cant assign a discrete countable attribute (such as the number of rows) to be infinity. infinity is not a number. saying the number of rows equals infinity is the root of the argument in this thread.

Clyde

08-31-2003, 01:46 PM

Even in that example, you don't can't say "I have infinite points, and therefore..."

In a given region of space how many coordinates are there?

kermi3

08-31-2003, 04:13 PM

In statistics if it has 0.0000% probablity it is impossible. However, in stats nothing ever has a true 0 possibility. In statistics possiblities are measured by the area under a probability distrabution curve. The most commonly used is the Normal curve (http://www.psychstat.smsu.edu/introbook/sbk11.htm). However, both ends of that curve end in asymptots so there is always some small area below the curve. Since the area under the curve is the probability at that point and there is always something under the curve because it never reaches 0 the proability of something happenning is never 0.

Make sense?

Zach L.

08-31-2003, 04:49 PM

Originally posted by Clyde

In a given region of space how many coordinates are there?

Read the next sentence in the post, and you'll see.

*ClownPimp*

08-31-2003, 07:59 PM

your triangle has an infinite number of rows. let 'n' denote the number of rows in your triangle.

now i'll define a new triangle with n+1 rows. my new triangle has more rows than yours yet yours has an infinite number of rows. obviously this is wrong.

assigning the number of rows of the triangle to n is assuming the number of rows is countable, which it isnt. So saying n is the number of rows is incorrect (thats why I changed my (feeble) definition of a triangle with an infinite number of rows).

[edit2]

Its like saying let the set of positive integers has n elements. Now make a new set of positive integers with all the elements from the first plus n+1 as the new element. And saying there is a contradiction in claiming the original set of positive integers is infinite

[edit1]

I just thought of a new way of thinking of a pascals triangle. Instead of thinking of it as a 'triangle', think of it as a set with each row of the triangle a member of the set. And use the method for constructing the triangle as the method for building the set. Just as the set of integers is infinite, the set of pascal's triangles' rows is infinite.

*ClownPimp*

08-31-2003, 08:21 PM

The problem with having an 'infinite number' of anything is that the term 'number' implies that the actual amount belongs to some set of numbers (Z, Q, R, C, ...).

In all the math classes Ive been in 'an infinite number' of something was always used to mean the number of something was not finite, meaning cant be counted (hence the term infinite)

Jeremy G

08-31-2003, 08:38 PM

Clarification time:

0% probability is an impossibility. FIN. THE END. COMPLETE. NO MORE DISUCSSION.

You all seem to be arguing over the same pascal example which I think is dumb - as I think the original assumption that its a 0% probability of picking an odd row is a flawed statement - the teacher was wrong - mis said what he/she ment or what ever.

I.e 1/0 is entirely differnt from 1/infinity.

novacain

08-31-2003, 09:19 PM

"Once you have discounted the impossible, whatever remains, no matter how improbable, must be the solution."

Sherlock Holmes (A C Doyle)

0 probability = impossible.

(just as an event with 1 probability will always happen)

1/infinity != 0 probability

(though it may be close enough for most observations depending on the accuracy required)

ie the chance of finding your car keys on a beach is close enough to be 0 but is not impossible.

Or the chance someone walks out of a casino with all their winnings, now thats impossible, trust me.

Clyde

09-01-2003, 01:32 AM

Read the next sentence in the post, and you'll see.

I did, but it doesn't answer the question.

You seem to be arguing that infinity as a concept does not exist.

So my question is, how many coordinates are there in a given region of space and what is the probability of choosing 1 at random?

I know you can tell me how the probability of choosing a number at random out of an ever growing pool of numbers is changes. But, that is not my question. Infinity might not be a normal "number" but it is something, and i do not see any invalidity in claiming something has an infinite "number" of X.

We use limits to aid us with infinities because they defy normal mathematical rules, that doesn't mean the concept is not a useful one.

Magos

09-01-2003, 05:14 AM

Originally posted by novacain

1/infinity != 0 probability

(though it may be close enough for most observations depending on the accuracy required)

You cannot divide a number with infinity. You can divide with a number n that approaches infinity, thus getting a number that approaches 0.

Zach L.

09-01-2003, 08:49 AM

Originally posted by *ClownPimp*

In all the math classes Ive been in 'an infinite number' of something was always used to mean the number of something was not finite, meaning cant be counted (hence the term infinite)

Okay, we agree. What you call an "infinite number", I'd call "infinitely many" to distinguish it from numbers... but thats kind of irrelevant.

Clyde, I'm not arguing that the concept of infinity does not exist, I am stating that it is not a number. You cannot add, multiply, subtract, divide, or otherwise use it as any number. There are infinitely many points in a given region of space (disregarding Planck-length, etc), and the limit of the probability function is 0. Infinity is a quantity that is larger than any real number, and hence, it is not a number.

Silvercord

09-01-2003, 03:48 PM

WE SHOULD START TALKING ABOUT GOD NOW TOO

christ

no pun intended

if that was even a pun

im just going to stfu, bye

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