No, Jaff is right.

0.9 reoccurring is not equal to 0.98, or 0.999999999999998, or any other iteration thereof.

The 'decimal representation' of Pi, as you say is 'infinite'. This is different to what infinity is.

The answer to Sacrieurs initial problem is zero. Since infinity is implausible, it is fitting that the probability of picking a 42 from infinity (or an infinite set of numbers) is also implausible, and therefore zero.

There is no end to the decimal representation of pi.

Is 1.000...0001 equal to one, cardinal?
It is.

That number is the difference between 0.999...999 and 0.999..998, which is not an "actual" difference.

I mean it is a "difference" but it's infinitely small.

That's why it was in quotes. It's the same reason why there's "no end" to 0.999...

I think there's a lot of statements that can be made or argued. Many of you are just trying to take imperfections of today's representation of ideas (in this case, written math) and are representing them as logical insights when they are just failings of how we display perfect ideas with imperfect systems. Look at what I can do with the same logic that many of you impose:

ASSUMING:
Whereas, X is equal to the probability of selecting the integer of 42 out of all integers possible, in a perfectly and equally random environment. X has N probability out of infinity.
Whereas, Y is equal to every possibility of an appropriate integer that is not 42, and assuming that there are infinite integers possible. Y has every probability of infinity, save for one of them. (42)
Whereas, ∞ is equal to the coefficient or symbol of infinity, or infinite probabilities/possibilities. This means X and Y together must equal infinity.
Whereas N is equal to one possibility out of infinity, not necessarily but quite possibly 42. N and Y also equal infinity. X and N are equal in amount of probability in being selected out of infinity, as they both just represent a single integer in the random pool of integers ranging up to infinity. X however, is special and must only be 42. With me so far?

∞ - N = Y
∞ - X = Y
X = N
N + Y = ∞
X + Y = ∞

Y cannot equal infinity without X, if N is not present.
Y cannot equal infinity without N, if X is not present.
Therefore, N, and surely X as well, has significance to some sort of amount, or bearing, no matter how minimal.
To represent the very smallest amount in decimal, you must show a representation of an infinite amount of zeroes (0) before you show a representation of 1. This representation accurately shows what X's probability is.
(Spacer, the following underscore is to be above .000) ___
(As a decimal, total probability/possibility is 1) X = 0.000000001

From here on out, the variable P Is to be assumed as a representation of the decimal above.
X is not neutral, is not negative, but it is indeed positive.
1 > X > 0
P = X
1 > P > 0
1/∞ = P
1/∞ = X
X/∞ = (1/∞)/(∞)

I understand that. With 0.999...98 Vrael is making a claim that it ends with a particular digit that is preceded by an infinity of nines. Hence it ends at some point. Hence it does not have an infinitely long decimal part.

Sorry, it doesn't work like that. It doesn't "end" or anything. It's an infinite string of digits, but the last conceivable digit in infinity is an 8.

There is no difference between reaching the "end" * of .999...98 or reaching the "end" of pi. They both exist, though for .999...98 its easier to simply write 1, and for pi its easier to write pi than 3.1415926535...

I suppose my point is that "managing to reach" a given number, as in write it in a finite amount of time, however large, does not negate the existence of a different, infinite number.

*Neither number actually ends, as you've said. They both continue on to infinity, I'm simply remarking on your "manage to reach the eight" which isn't possible.

There is no "managing to reach" a number in a string. If something is infinite, you can't read every digit as a human.

In a mathematical sense, you don't read every digit one at a time, none of this "Reaching" bullshit. We aren't an encouraging institute for cancer, asking children with disease to 'reach for the stars'. We're talking about mathematics. Rigorous, exhaustive mathematics. Or sex.

Anyways, If you're thinking with the sense that the ideas we represent and prove legitimately are perfect, as addition and subtraction is 'perfect', then a string of 9s after a decimal with an 8 after is an easily possible decimal within a mathematical spectrum. Humans "get through" digits to interpret and understand the meaning of the string of the number as a whole. Mathematics and the laws behind it does not. It knows the entire number or concept in the first place. Nature and mathematics, yo. And sex.

I am heartily confused about your mentions of sex. Do you have A question (or 2!) about sex?

9887 / 3838

Or was that it, I don't even remember

If X is zero, then Y can equal infinity. This premise is flawed.

X is not 0.
1 > X > 0, as previously stated.

9987//2323

Which you used your previous assumption to prove. Does this ring a bell:

Don't you just love context

They aren't the same at all. ;o There is a difference of .000...001. It's not infinite at all. The <...> is to be a finite, though arbitrary, number.

It's a misunderstanding then. We're using the ellipse to designate an infinite continued sequence.

I think JaFF has the best understanding of the matter here.. I don't know why everyone is so determined to argue about things that have concrete, well-understood meanings.

If we take the ellipses to mean an infinitely repeating string of decimal digits, there is no meaning to what comes after them, because they have no contribution to the number.

Thus "0.9...9" equals "0.9...8" equals "0.9...{anything you want to put here}" and all are identically 1. Similarly, "0.0...1" is equal to "0.0...{anything you want}" and all are identically zero. There is no interpretation, semantics, etc. This is mathematical fact.

Similarly, the probability of choosing 42 out of the set of integers is identically zero, and the probability of not choosing 42 is identically 1.

If the ellipsis is infinite number of digits, how would anything come after it? ;o

The challenge was proposed to display such a number. I had said that it has no meaning, and is genuinely worthless.

If that thing was equal to zero, that's how. Which is precisely the case of the above. I think some insight can be gained from looking into it. It's proving that the only thing that can come after an infinite number of digits is anything that is equal to zero.

[Removed fallacious argument.]

Post has been edited 3 time(s), last time on Nov 18 2011, 9:07 pm by Sacrieur.