# 0% probability == impossible?

This is a discussion on 0% probability == impossible? within the A Brief History of Cprogramming.com forums, part of the Community Boards category; >> The fact that the triangle is assumed to have an infinite number of rows ... While it is true ...

1. >>
The fact that the triangle is assumed to have an infinite number of rows
...
While it is true no one can never enumerate infinity,
<<

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.

2. 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.

3. 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."

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

5. >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.

6. 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.

7. >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.

8. >> 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.

9. 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:
Code:
```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

10. 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.

11. >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?

12. 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...

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

What?

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

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

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

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