Come on, you can get this!
2006-09-14 02:29:08 · 20 answers · asked by Rockstar 6 in Science & Mathematics ➔ Mathematics
You can't do math saying "upto n digits" because that would be placing a limit on an infinitely defined number.
2006-09-14 02:29:53 · update #1
I didn't say that 1/3 - 0.3333
I said 1/3 = 0.33333... The threes go on for forever.
Do it on your calculator dammit
2006-09-14 02:39:35 · update #2
For ease of typing, .999 shall be equivalent to .9 repeating as in it goes to infinity.
Let X = .999; simple declaration
10X = 9.999; multiply both sides by 10
10X - X = 9.999 - .999; subtract the same value from both sides of the equation
9X = 9; simplfy
X = 1; divided both sides by 9
.999 = 1; X=.999 and X=1 therefore .999=1
recall that throughout this proof the number of 9's in .999 is infinite, anyone that argues the logic of this obviously does not fully grasp the concept of infinity and is wrong.
Ok well I looked at your other question and apparently you already knew what I just typed so I basically wasted my time :(
2006-09-14 02:53:15 · answer #1 · answered by Justaguyinaplace 4 · 3⤊ 1⤋
3
2006-09-14 02:30:47 · answer #2 · answered by Anonymous · 0⤊ 1⤋
In fact you are correct. For example, if we have two digits, .99 = 1-1/(10^2) and for three digits, .999 = 1-1/(10^3), etc. So if we have n digits, .999...n = 1-1/(10^n) and if we look at the limit at n goes to infinity 1-1/(10^n) = 1, so .999... = 1. This was proved by Euler in the 1700s. We really don't need a mathematical proof, though, because we have implicitly made a definition when we write something like 1/3 = .333..., thus they are equal by definition, they are DEFINED as equal, only the symbols are different.
2006-09-14 03:09:22 · answer #3 · answered by 1,1,2,3,3,4, 5,5,6,6,6, 8,8,8,10 6 · 2⤊ 1⤋
The actual way to write 1/3 in decimal is form is 0.3 with a bar over the three (the computer won't actually let me do this, so I'll write it 0.3... for lack of else). As stated above (and as I learned in an algebra class in high school):
x = 0.9...
10x = 9.9...
subtract the first equation from the second equation:
10x - x = 9.9... -0.9...
9x = 9
x = 1 and since I established x = 0.9...,
then 1 = 0.9...
If you work it with fractions, you get the same thing with 1/9 x 9 = 9/9 = 1
As crazy as it sounds, 0.9... is the same thing as 1.
2006-09-14 03:01:33 · answer #4 · answered by The Doctor 7 · 2⤊ 1⤋
you were doing so well...right up until
0.9999...=1
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 02:31:37 · answer #5 · answered by Morgy 4 · 0⤊ 3⤋
Look at it this way.
If you have an equation that contains, say 1/4, you can replace that with 0.25. That is an exact representation of the fraction. However, if you have an equation with 1/3 in it, you leave it in that form because you cannot represent that fraction exactly as a decimal.
You have to be careful when dealing with infinity. As I've said before, not all infinities are equal.
2 x infinity = infinity is not valid math.
2006-09-14 02:54:06 · answer #6 · answered by Dan C 2 · 1⤊ 2⤋
Yes you are right. But 0.3333 is not 1/3, it's a little bit less and you'll never reach 1/3 because decimals aren't designed that way. The very word 'decimal' means of a tenth part. 10 is not divisible by 3 in whole terms except in fraction form so as the comparison is not of equivalent values it is not valid.
2006-09-14 02:38:51 · answer #7 · answered by quatt47 7 · 1⤊ 4⤋
Who told you 1/3 was 0.3333
2006-09-14 02:35:00 · answer #8 · answered by A 4 · 0⤊ 3⤋
Yes you are correct, and your reasoning makes sense. Another way to think about it is that if 0.9999... is not equal to 1 there has to be another real number between them, but there is no number between the two, so they're one and the same.
2006-09-14 02:44:15 · answer #9 · answered by Kyrix 6 · 5⤊ 1⤋
0.9999... is never equal to 1 no matter how many ACTUAL times you write a 9.
0.9999... is always equal to 1 when the dots mean keep going to infinity.
People who mix these two different ideas up are going to always be wrong.
2006-09-14 03:35:18 · answer #10 · answered by Anonymous · 1⤊ 2⤋