I mean the 9's go on forever, so would the difference not be infinitely small? The only number that is infinitely small is Zero. So the difference should be zero. The only way to say there is a difference is to do the human thing and subconsciously assume that the 9's end somewhere. This begins to explain how we really cannot comprehend infinity, even with one simple number.
2006-09-11 04:15:30 · 24 answers · asked by Rockstar 6 in Science & Mathematics ➔ Mathematics
The other thing is that .99999.... isn't a real number. It's only a figure derived from our own mathematics. Or is it?
I challenge you to find a way to prove that there is a finite definition to any measurement in nature. The problem is that we have limitations on our measurement and our brains and willingness to go on.
2006-09-11 04:17:10 · update #1
If the zeros go on forever, then there's no room for that extra 1 in there, is there?
2006-09-11 04:20:13 · update #2
Though quarks are the smallest component, we could still measure smaller. Infinitely smaller.
And as for the measure of the speed of light. suppose there was a .0000000001 margin in that measurement. We only measured it to the best of our abilities. We could probably measure it even further than that.
2006-09-11 04:37:01 · update #3
Mathematically, 0.99999... is considered to be exactly equal to 1. The formal proof (greatly paraphrased) goes something like this:
- Take any number epsilon (greater than zero).
- No matter how small you make your epsilon, I can produce a number n such that 1 - 0.99999..., with n nines, is less than your epsilon.
- Therefore, no matter how small your tolerance limit for "anything bigger than this is different enough for the difference to be significant", the difference between 1 and 0.99999... (ad infinitum) is smaller than that.
- Hence, we consider 1 and 0.99999... to be equal.
Additional details:
0.99999... is a real number. It's equal to 1, which is a real number. Don't get hung up on the infinite decimals... we consider pi to be a real number too!
As for your "finite definition to any measurement" thing: No matter how small you make your epsilon - your arbitrary limit on "if the difference is smaller than epsilon, we consider the two things to be the same" - it may be at least theoretically possible to come up with a measurement more precise than your chosen epsilon.
There's room to wax philosophical about this stuff, but the argument that "at some point, the difference is so small it can be ignored" is one that mathematicians do use.
2006-09-11 05:26:09 · answer #1 · answered by Bramblyspam 7 · 2⤊ 1⤋
The only number that is infinitely small is Zero.
Who say so? Think again. If you can have one infinitely small number, then why not two or more. If you can have more then two infinitely small numbers, then 1 and 0∙999999.... will never have the same value and so the difference is not zero.
Start thinking in terms of infinity and compare the numbers together. They do not have the same value.
The other thing is that .99999.... isn't a real number. It's only a figure derived from our own mathematics. Or is it?
All numbers are derived form our own mathematics, numbers are basically what you when them to be.
We may have limitations on our measurement equipment, but the limitations on our thinking is what we put on it.
If the zeros go on forever, then there's no room for that extra 1 in there, is there?
If any of the zeros are changed to a 1, then there's plenty of room for it.
The more accurate out measuring equipment becomes the more accurate will our measuring potential become. Then of course the speed of light could be measured with better accuracy.
2006-09-11 07:16:41 · answer #2 · answered by Brenmore 5 · 1⤊ 1⤋
All those people who claim they can prove that 1 and the other thing are equal are using faulty logic. One cannot simply subtract one unending number from another. Subtraction works only for finite numbers (either in and of themselves or from rounding off).
What we are dealing with here is one of the major weaknesses in mathematics...infinity. Infinity is simply not a number. It does not follow the simple math operations like add, subtract, multiply, and divide. What does 2 X infinity equal, for example? (Work this out and you can "prove" that 2 = 1...totally ridiculous.)
Mathematicians have been trying to deal with the infinity concept for centuries; but their solutions are only workarounds that work in special cases. The Dirac delta, for example, can be invoked when solving equations that are well behaved as they approach a singularity point (a point where things blow up to infinity).
Anyway, the bottom line is this, beware of any so-called proof that invokes infinity in all its guises, including an infinitely long number like .9999999999999......
2006-09-11 05:39:15 · answer #3 · answered by oldprof 7 · 0⤊ 1⤋
Of course there's a difference. If there wasn't a difference then the two things (1 and .9999...) would be equal.
If what you're saying is true then it would be impossible to explain loads of things...
For example, assume a person is 1 metre from a wall, and they move half that distance closer to the wall, then they are 1/2 a metre from the wall.
If they then decide to move half the remaining distance they would be 1/4 of a metre from the wall.
If they then decide to move half the remaining distance they would be 1/8th of a metre from the wall.
Using your logic this would go on for an infinite series of steps and the person would never actually reach the wall.
Stop over thinking it.
As for your challenge to find a finite measurement in nature:
1 metre is the distance that light travels in 1/299,792,458 of a second
EDIT:
Would you stop saying that about rounding.
I'm telling you that in nature the distance that we refer to as 1 metre is the distance that light travels in that length of time. There is no rounding error. It's nature.
There may be an error in how we record time or distance but that doesn't remove the fact that there are some actual exact constants in nature, one of which I refer to above.
As for the quark guy, people didn't use to think that there were things smaller than atoms. Then we discovered quarks. It will only be a matter of time before we discover something smaller.
2006-09-11 04:25:45 · answer #4 · answered by Truth speaker 2 · 0⤊ 4⤋
You ask for proof of a finite measurment in nature. Well everything in nature is made up of finite objects known as quarks which form together to make atoms. any measurement of matter must be in whole units of quarks so there must be a smallest measurement therefore the difference between 1 and .9999... is the same as the width of one quark.
2006-09-11 04:30:36 · answer #5 · answered by bretttwarwick 3 · 0⤊ 0⤋
The difference is 0.00000 (the zeros go on forever) with a 1 at the end.
no, there isn't room for the extra 1 in there. Thats why the're equal.
I hope that settles it.
2006-09-11 07:27:34 · answer #6 · answered by davidosterberg1 6 · 0⤊ 0⤋
The difference between 1 and .99999
=1-1/100000
SO,IF WE GO INFINITELY , THE TERM 1/10000....BECOME SMALLER AND SMALLER SO IT CAN BE NEGLEGIBLE.THE LIMIT OF DIFFERENCE TENDS TO ZERO.
IF YOU GO THAT MUCH IN DEEP , YOU MAY DISCOVER SOMETHING NEW.
THATS SURE!
2006-09-11 05:11:57 · answer #7 · answered by Anonymous · 0⤊ 0⤋
difference is 0 when 9 goes on for ever
when .9 goes on for ever the value = 1
say x = .99999.......
10x = 9.99.........
subtract 1st equation from 2nd 9x = 9 so x =1
Note:
People do not feel uncomfortable when we say
1/9 = .1111111....
but they feel uncomfortable when 9/9 = .999999...
However if it stops after n 9's then difference = 10^(-n)
2006-09-11 04:58:48 · answer #8 · answered by Mein Hoon Na 7 · 0⤊ 1⤋
alot... .0 (going on forever with a 1 at the end) what the diffrerance between 1 and .9 = .1
Tex
2006-09-11 04:20:25 · answer #9 · answered by Tex 2 · 0⤊ 2⤋
You can actually prove that .99999... equals 1. Check it:
x=.9999....
(multiply by 10)
10x=9.99999....
(subtract x=.9999....)
9x=9
(divide by 9)
x=1
2006-09-11 04:17:50 · answer #10 · answered by hslayer 3 · 2⤊ 1⤋