(10-07-2012, 12:03 PM)Googolplex Wrote: The problem is, that 1/3 is a little more than 0,3 (infinite 3), but a little less than 0,3...34.
So, the correct number is between that, but there's no wise to scribe it.
The periods are only existing between thoughts. When I say 0,9 (infinite 9) I can't calculate this number, because no calculator can handle infinite numbers, and so the end result will be wrong. The calculator will round the numbers and put put a wrong result. You can only calculate in theory, with the knowledge, infinite 9 is "equal" to 1. And 3x (1/3) is exactly 1 and not 0,9 infinite. You can't simply multiply or divide the numbers, you must know that the exact result of 1/3 is more than 0,3 infinite. And by multiplying with 3 it will not be 0,9 infinite, it will be 1 again.

(10-07-2012, 11:00 AM)BAndrew Wrote: 1)My point was that a computer is a more powerful calculator as it does much more things than a calculator, so I will leave this here.

2)I read your post. I agree that a computer cannot calculate infinite digits (like Pi as you said),but what I am trying to tell you is that it doesn't actually calculate them. It uses (let's say) mathematical tricks in order to get the result. It can't calculate Pi itself.

3)We just proved that it is the same number. It's like saying what's the distance from 2 to 2. Unless your are talking about complex numbers and not real numbers that statement doesn't make sense to me.

(10-07-2012, 12:21 PM)Bridge Wrote: 3) Stephen Hawking also "proved" quite efficiently that the universe is not infinite but that's only because it cannot possibly be measured now. Laws are based around the knowledge we have at any given point in time, and laws have to be changed and revised constantly to accommodate new advances in science. Before the theory of relativity was developed for example scientists probably believed any speed attainable whereas now we know that anything with a positive mass is confined to speeds below the speed of light (e=mc^2). I don't doubt that 0.9~ is provably 1 but just like quarks are now measurable perhaps the real distance between 0.9~ and 1 will be measured at more than 0 in the future. Before quantum mechanics were invented, nobody would have imagined anything smaller than an atom but now we know that matter is constructed of particles even smaller than quarks.

All I'm saying is that it's possible we will be able to calculate the difference between 0.9~ and 1 some day; you even said it yourself: it's infinitely small. Maybe infinitely small today, but what about tomor

(10-07-2012, 12:26 PM)BAndrew Wrote: There is difference bewteen 1 and 0,99999. It is mathematically proven and that won't change no matter how small scales we are going to discover.

(10-07-2012, 12:29 PM)Bridge Wrote: Don't be so conservative. I just gave two examples where a theory set in stone so to speak was disproven overnight. What right do you have to dictate what the future may hold? Just because you can prove it with the knowledge we have now doesn't mean it is absolute.

EDIT: Furthermore, all of the arithmetic operations you performed on the algebraic equation x = 0.9~ are incompatible with infinitesimals. There is something between 0.9~ and 1; current mathematical rules simply cannot account for something so small.

(10-07-2012, 12:39 PM)BAndrew Wrote:

(10-07-2012, 12:29 PM)Bridge Wrote: Don't be so conservative. I just gave two examples where a theory set in stone so to speak was disproven overnight. What right do you have to dictate what the future may hold? Just because you can prove it with the knowledge we have now doesn't mean it is absolute.

EDIT: Furthermore, all of the arithmetic operations you performed on the algebraic equation x = 0.9~ are incompatible with infinitesimals. There is something between 0.9~ and 1; current mathematical rules simply cannot account for something so small.

It's not a theory and I am not conservative. It's a proven fact. Mathematics can't be wrong.


See the analytical proof which is the right one and it is accepted by mathematicians. The others are simplified.

(10-07-2012, 12:47 PM)Bridge Wrote: Yeah I saw the proof and I don't accept it. Lim n->inf 0.{00.....001} (n-1) = 0 is a loss of data. There is a trailing 1 there, it is just not calculable at this point. I don't give a shit whether it works according to the current system, the fact is mathematics require concrete rules to work, and there are no rules for infinitesimals at this time. Mathematics are not absolute, no matter how much you want them to be.

EDIT: You do realize you can prove anything if you violate Occam's Razor, right?

(10-07-2012, 01:06 PM)BAndrew Wrote:

(10-07-2012, 12:47 PM)Bridge Wrote: Yeah I saw the proof and I don't accept it. Lim n->inf 0.{00.....001} (n-1) = 0 is a loss of data. There is a trailing 1 there, it is just not calculable at this point. I don't give a shit whether it works according to the current system, the fact is mathematics require concrete rules to work, and there are no rules for infinitesimals at this time. Mathematics are not absolute, no matter how much you want them to be.

EDIT: You do realize you can prove anything if you violate Occam's Razor, right?

Lim n->inf 0.{00.....001} (n-1) = 0 is NOT a loss of data. It is proven through Archimedean Property .

(10-07-2012, 01:21 PM)Bridge Wrote: I may not know as many fancy names as you do, but when I have something, and then suddenly I have nothing, I consider that a loss of data. End of story. Plus:

"An algebraic structure in which any two non-zero elements are comparable, in the sense that neither of them is infinitesimal with respect to the other, is said to be Archimedean."

0.00 … 1 is infinitesimal in regard to 0.