0.999... = 1?????
Question: And I think I can prove it.
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... denotes an infinitely repeating decimal advantage.
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1. Set c = 0.999...
c = 0.999...
2. Multiply both sides by 10.
10 * c = 10 * 0.999...
3. Simplify.
10c = 9.999...
4. Subtract c from both sides.
10c - c = 9.999... - c
5. Substitute 0.999... for c on the right side.
10c - c = 9.999... - 0.999...
6. Simplify.
9c = 9.000...
7. divide both sides by 9.
c = 1
8. Since a variable next to an assigned value can singular equal that value, and c be set equal to 0.999..., but we just determined that c also equals 1, c = 1 = 0.999...
This resources that 1 = 0.999...
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I know that an article on this topic was just now featured on a unquestionable online encyclopedia, but I came up near this proof on my own. So, flame my math, not my originality.
Answers:
It's certainly a simple error in rounding. Look at it this track: If you have 10 of these ".99999..." objects, and you subtract one, you're disappeared with 9 ".99999..." objects. 9 ".9999." objects are exactly what you hold on both sides of the equation before you divide by 9, and so each side of the equation contains one ".9999..." after the division by 9.
More or smaller number, this is basically a prime example of the danger of the rounding errors that can occur when using infinite decimals. It's of stress to note, however, that this type of rounding error matter none in any practical application of reckoning, as it's impossible to define a amount of accuracy that contains an infinite amount of decimals. This is a rounding error that matter purely in the empire of theoretical sums.
well done!
you be brilliant to know that, i don't know how much one plus one is?
I shall sleep soundly now......
Great!
why don't you use infinite geometric series
r=1/10
a=0.9
Sn = 0.9+0.9*1/10 + 0.9 * 1/10^2 + (0.9*1/10^2) .
Summation of Infinite geometric series = a / 1-r = 0.9 / 1-1/10 = 0.9/0.9 = 1;
Excellent, but it solitary works in the "limit" sense. Here is why:
.999 x 10 = 9.990, not 9.999
9.990 - .999 = 8.991, not 9
If you allow c=.9999999999999999999 forever, afterwards you are describing a "limit" function, not a number. Certainly, the limit of 9.9999999 going on forever IS equal to 1.
See: Limit (mathematics) at http://en.wikipedia.org/wiki/limit_(math...
Wonderful.
You know in fact you have proved zilch, this is all base on the basic assumption that current geometric principles are true. try proving that 1+1=2 without making an assumption, for example are adjectives values of 1 the same? The age ancient principle of proof has be going on for a very long time, adjectives you can actually say-so is that you have implied that, or suggests that; proof is total. Your mathematics may be immaculately deduced, your reasoning nouns, but all you own done is shown according to current knowledge not proved it to be true
another style;
0.33333..=1/3
3*1/3=1=3*0.33333...
=0.99999....
and so on
i hope that this helps
I did that ages ago..
See it thus
1/9 = 0.111111...
5/9 = 0.555555...
7/9= 0.777777..
:.9/9 = 0.99999..
but 9/9 = 1
.: 1 = 0.999999...
Your proof is not valid as you cannot do a proof by using both sides. You enjoy to go disappeared to right of vice versa. There is also a proof of 1 = 0 can't remember it at the moment but it works the same instrument as yours and is invalid for that reason.
Congratulations. You merely showed that decimal expansions are not unique. Yes, you are correct.
Your wrong
10c= 9.99 NOT 9.999 as You suggest
Clever, I option could do that
Sorry, but the maths is not quite right! If you pilfer the sequence 0.999 to infinity, the number 1 will still be the next complete biggest number. That is the point of infinity. You can only go and get there surrounded by your mind.
couldnt you prove that all numbers = 1 surrounded by the same channel, humans came up next to maths its just a flaw contained by our creation
This is very clever, and can be added to the several other proofs for this theory.
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