The difference would be 0.0000... with zeros going on forever and a one at the end right? Well, where does the one go? At the end of forever??? That's a paradox. There's no end to forever, therefore, there's never any ones. We tried to prove it with math, but you couldn't see the whole picture, so you used rounded numbers which changed the whole equation. Think in terms of infinity.
It really is difficult for the mind to grasp infinity, though, isn't it. Even with one simple number.
1 and 0.99999... are one in the same. Any reasoning used to try to say "the difference is there, it's just ininitely small", is faulty reasoning, as "infinitely small" is by definition, zero.
2006-09-14 02:03:44 · 16 answers · asked by Rockstar 6 in Science & Mathematics ➔ Mathematics
Just for reference, here's the math we used:
Let X =0.99999... So 10X = 9.99999...
From this we derive that 10X - X = 9X = 9.9999... - 0.99999... = 9
Thus, 9X = 9, and finally, that X = 1, not 0.99999...
Thanks to, um, Al Gore...
2006-09-14 02:05:18 · update #1
Ok so it was Fermat's Last theorem.
2006-09-14 02:05:47 · update #2
Sorry that math was wrong:
x = 0.99999...
10x = 9.99999...
10x - x = 9.99999... - 0.99999...
9x = 9
x = 1, not 0.99999...
2006-09-14 02:09:19 · update #3
I'd like to differ with you, if I may. You spok of being off in your tragectory, but my arguement is, that even if you're coming from the other side of the universe, or 4 times that distance, that number is still finitely definable. You would have to retrace a path that went on for infinity to find the place where that number would ever matter, which means you would never stop looking. You would never find that point where it would throw you off. Ever. In order to say that it would matter, you would have to put a limit on the number, somewhere, even if it's 400 googol zeros beyond the decimal point. 600 lengths of the universe, that's still a finite number. So if the distance is forever, then there's no end, and no place for a number at the end. The words "however small" relates only to a number that has an end to it. You can keep going to infinity and stopping at points along the way, and say "This small...or this small?" but, I don't know how to further express the fact that there is
2006-09-14 02:26:45 · update #4
I've been thinking about why there is so much resistance to this equality, and I think a lot of people are unknowingly using a different number system than us. There is another number system out there which is consistent in its own way, but includes "infinitesimal numbers", ones which are smaller than any fraction, for example. See my source for a description of this non-standard number system. Now if your intuitive picture of numbers includes infinitely small numbers, it is possible to have numbers like .999999... and 1 which are "infinitely close but not equal". How to resolve this dilemma? Perhaps we should just continue using our number system, and let them use theirs, and just recognize that their math has different rules than ours. And that's okay.
2006-09-14 05:12:35 · answer #1 · answered by Steven S 3 · 1⤊ 1⤋
I think someone has a problem with inf numbers... .999... repeating forever does not a 1 make. At least not if you're useing a form of math and logic. And while you cant actualy express .999... that doesnt mean you just give up and say its 1. The number .999... while being so close to 1 it would take forever to figure out the difference that does not mean there is no difference. Also all of these math problems have one major flaw in them... The +/- and such are made up concepts they dont actualy exist. So when ever you use them you are actualy inventing something that did not exist before imo. The universe flows like an ocean not some type of matrix where everything can be paused and counted then started again.
2006-09-14 09:51:23 · answer #2 · answered by magpiesmn 6 · 0⤊ 1⤋
Infinitely small does not mean zero. Zero is basically the reciprocal of infinity but infinity is not as easily definable. It is often a limit, the limit of the real number system.
With your supposed "proof" when you multiply by 10 the (n+1)th digit at the end is ignored but it'll always be there, unlike fractional values where a limit may be evaluated in a similar way decimals are a whole lot messier.
So quit justifying your calculator, mathematics is so much more than calculation.
2006-09-14 09:43:45 · answer #3 · answered by yasiru89 6 · 1⤊ 0⤋
there is a problem with fermat's last equation in terms of minute (i.e. very very small)particles...
you see
when u say X=.99999... say upto n digits and
then 10X= 9.9999 will be upto (n-1)digits
so 10X-X= 9.99999...(n-1 digits) - .99999 ....(n digits)
9X = 8.9999(n-1 digitsof 9) ...1
then X= .99999(upto ndigits of 9).
which is not equalent to 1because when you want to say 100% of a substance is soluble or even present in a substance then in this case we only 99% what about the remaining 1%. what happens to 1% is important.... so this concept is still in speculation.
2006-09-14 09:21:57 · answer #4 · answered by azeem 2 · 0⤊ 0⤋
ah, engineering maths.
infinitely small is not the same as zero. zero is zero.
.999999... and 1 are NOT the same.
.9999... = 0.9999... and 1=1. Different things.
From the purely mathematical point of looking at 'number', they're different things.
What number lies between 0.9 and 1?
0.99
what number lies between 0.99 and 1?
0.999
etc etc
It doesn't matter how small the difference gets, there's still a difference there. And if there's a difference, that means they're not the same.
You can use the *approximation* for calculating things, for simplifying formulae, but it's still wrong to mathematically define 0.9999... = 1. It's just wrong.
2006-09-14 09:27:15 · answer #5 · answered by Morgy 4 · 1⤊ 1⤋
I've seen this before. While I appreciate the "point", and I do "get it", I think I'd still prefer to think of this as an asymptote.
After all, it never ACTUALLY reaches the whole number, we just consider it "close enough not to matter". Asymptote, on the other hand means almost the same thing, but IMO is a more accurate description. No information is lost, however trivial.
2006-09-14 09:13:46 · answer #6 · answered by Dan C 2 · 1⤊ 1⤋
sorry, but if you out things into real-world scenarios, you will find that regardless of the number of decimal positions to the right, it does not make the next "whole" number, unless you round up.
in space and time, if you were off by that .000000001 then you can overshoot your destination by a nearly infinite distance, depending upon the distance from your start point, to your destination end, due to trajectory errors.
to the average person, and to me as a scientist in my "normal" world outside of the office, i use "1.0" but when it comes to being correct, no matter the infinite number of reciprical "9s", the answer is still NOT the next (rounded up) whole number.
-eagle
2006-09-14 09:14:34 · answer #7 · answered by eaglemyrick 4 · 0⤊ 1⤋
Keep in mind that .9999999... doesn't "equal" 1. However, the limit of the geometric series is 1.
In other words,
lim_{n \to \infty} 9 \sum_{i=1}^n (.1)^i = 1
That's the real difficulty. We're talking about a limit.
2006-09-14 09:11:40 · answer #8 · answered by Ted 4 · 1⤊ 2⤋
Because it's not. It's close, but not equal. the only thing equal to 1 is 1. That's it. I can say "Well, I almost won the lottery", but they won't give me $100 million, now will they?
2006-09-14 09:09:40 · answer #9 · answered by Jason J 2 · 2⤊ 2⤋
because apparently 1 and 0.999999..................are different.
o is a concept to denote something insignificant
so 1-0.0000000000000000000000000....
will be like subtracting 0 from 1 and so is 1
2006-09-14 09:08:21 · answer #10 · answered by raj 7 · 0⤊ 1⤋