0.999 exactly equal to 1?

X = 0.9990
10x=9.990
10x-1x=9.99-x
9x=9.990-0.9990
9x=8.991
X=0.999

 

There is a huge flaw in this. You're redifining a variable which is set to a constant. Once you equate 'X' to .999 you thereby make 'X' a constant and not a variable. Therefore your equation does not equate.

Now, the more logical way of doing this is as follows.

1/9 = .111 repeating
1/9 * 9 = .111 * 9

9/9 = 1 = .999 repeating

Either way it does not mean that 1 = .9999. For to think so would be a flaw of logic. Also, because decimals that end with a repeating 9 are typically rounded because of this.

 

kk maybe i'm just really high, if so excuse me, but

Let x=0.999
10x = 9.999
10x - 1x=9.999 - 1x
9x = 9.999 - 1x
10x = 9.999
x = 9.999/10
x=0.999

now i don't know what you're trying to get at by solving for x... x is what it is, of course!

you said x = 0.999, and then proved it does.

 

haha reading through the posts i see this proof has been beaten to death

 

What you're missing is the

10x-1x= 9.999-1x because that translates into 9x = 9.999 -.999 which is how he gets

9x = 9

but again x was set as a constant .999, therefore it cannot equate to 1

 

Well the two problems that people are having here are that one, half the people posting here clearly have no idea what a repeating decimal is, and two nobody has explained the theory involved in the equation. A repeating decimal (for those who don't know) is a decimal which repeats the same sequence of intergers through an infinite number of places. Not five hundred or one thousand or some large thought finite number as kar33m seems to think, but in fact an unending series.

The reason that .9 repeating is virtually equal to 1 is that the difference between it and 1 is infinitely small. To illustrate; the difference between 1 and .9 (non-repeating) is .1, or 1/10, the difference between 1 and .99 (non-repeating) is 1/100, the difference between 1 and .999 (non-repeating) is 1/1000, and so on and so forth. However, in the case of 1 and .9 repeating a real number representational fraction is impossible since the decimal does not terminate. If one were to attempt a representational fraction it would look like this 1/10^infinity which indicates that the difference between 1 and .9 repeating is infinitely small, and now we get into the realm of imaginary numbers, which I will avoid.

1 and .9 repeating can be treated as being arithmatically equal. Even so this does not mean that they are in all ways identical.

 

thank you finaly someone who knows about math has come and saved u all from looking teribly fake and like a big set of posers .9 repeading is arithmaticly equal to 1 this is true so u can treat them as the same number because the difference between is so small and getting smaller but the second so it comes to point where the human mind can no longer truley apriciate how small it is this happends alot when one is trying to deal with the thought of infinity this also goes back to the riddle if u go from ur current location to half way to you destination and keep repeading this u basically are being the .9 repeating to the 1 where u can never reach ur final destination because u always go half way but eventualy u say u got there this is the same idea where u get so close to one that u basicaly are there

 

Yea one of my math teachers in high school proved, using a similar equation, that 1+1 = 1. And there's nothing wrong with the equation so you can't disprove it. That's why even simple arithmetic can be such a mindfuck.

 

10X = 9.99

Anyway, what you read was probably that the repeating decimal 0.999...9 is
equivalent to 1, which it is. It's one of a variety of math problems involving limits. Another example is the infinite halving of the distance between two points. The more often you halve the distance, the smaller the distance becomes, but you never reach the second point, except theoretically at the infinite limit.

 

While you're at it, here's a question that abuses math to the point of inanity: "How cold is twice as cold as 0°?"

 

You were doing OK until you failed to avoid the topic of imaginary numbers. An imaginary number is some multiple of the square root of -1. Since every real number, regardless of whether it is positive or negative, multiplied by itself yields a positive result, there is not real number that can be the square root of a negative number.

There are also complex numbers, which you get when you add together real and imaginary numbers.

There'snothing imaginary about these numbers, except the name. Without them, whole branches of physics, particularly the quantum field, would cease to exist as calculable entities.

 

So nobody has jumped off the deep end into either
rounding
or
digital readouts (which are at best +/- the least significant digit).


Nobody with R/L experiences? *c*

 

The moral of this lesson is, don't go down that path if you cain't do the math, doo-wop-doo-wop-...

 

1= 0.99
its all true i'm afraid

this is a tough one beyond my ken i'm afraid

but......my own problem with recurring numbers is this.

1 divided by 3 or 0.9 recurring (for example) is an expression of accuracy rather than the actual number i suppose.

when a number is recurring it has no finite value, can it be used with a type mathematical principles using finite values to get a finite logical answer??

1 = 0.99.. is not true because we are using the constructs of mathematics using finite numbers mixed with infinite values. when we use recurring decimals and numbers that are infinite we get answers that approach the true value but not actually the true value.

1 cannot equal 0.99 the equal sign proves this. if you sat down in a maths class and said 15 = 46 the maths teacher would mark you down as wrong!! argue with the equals sign not me. the fact that the equals sign is disagreeing with the two values led me to the realisation that finite values and infinite values used in a expression will give answers approaching the true answer but not actually the answer!! go figure. i've tried to. i would say 1 is approximately 0.9 recurring.

my argument follows this train of thought...

n appox 0.9.... (as a recurring value cannot have any finite value)
10 appox 9.99..
9n appox 9
n appox 1
1 appox 0.9 recurring

we are dealing with approximates

ps
i'm no maths genius so feel free to tear these thought to shreds!!!

 

what i'm trying to say is that the numbers being used are not compatible...

1n = 0.99999 cannot be used together

i say its more appropriate to say
1n is approximate to 0.99999

in the same way 1/3 is approximate or 0.333.. is approximate

when we use these numbers it would seem that out accuracy is limited to our use of them.

 

you see 1/3 is --- 1 a number with a finite value (no decimals trailing off to infinity)
divided by
3 a number with a finite value (no decimals trailing off to infinity)

gives a number that gives a value that trails off to infinity

(

n = 0.999....

i suppose it is ok to use the equal sign if you are dealing with purely finite numbers but not ok if we use numbers that have no finite value. we cannot use the equal sign between "n" and 0.999.... if any calculation is going to achieve any accuracy. )

for example if you were using this "logic" (1 = 0.9) in a computer on board a spacecraft to the moon i can guarantee that the spaceship would never reach the moon.

1 cannot equal 0.9999
1 can be approximately equal to 0.9999....

i suppose we could say 1 = 0.9..... + 10 to the negative power of infinity?

to make 1 = to 0.9 we must add 0.1 , or 10 power -1
to make 1 = to .99 we must add .01 , or 10 power -2
to make 1 = to .999 we must add 0.001, or 10 power -3 (try it on your calculator)
to make 1 = 0.99999999 we must add 10 power -8
to make 1 = 0.9....we must add 10 power - infinity?

therefore 1 = 0.9 is an incomplete ahhh.. truth...?????

rather it is 1 = 0.9 recurring + 10 power - infintity.


ok.... what if....

"n" is a finite number - and we give it a signifier showing it is such - like this

n*

0.999 recurring is an infinite number we give it this symbol "?" to represent it to get 0.9?

1n* = 0.9?
10n* = 9.9?

10n* - 1n* = 9.9? - 0.9?

9n* = 9.0?

n* = 9.0? / 9*( 9 retains its * symbol to show it reprents a finite number)

n* = 1 ?/*

therefore 1?/* = 0.9?

any maths maths teachers out there i'm probably wrong?

you see i say you can't mix these original values without modifying them to show that they are different kinds of values. any answer you get by mixing different kinds of values are approximate?

i'm probably way off track but there you go thats the beauty of independent thought, if its wrong!!!

 

maybe i should post this else where
maybe some crazy maths forum, i'm sure they'll me tell if its right or wrong?

any takers here?

i've made these threads separate to show my line of thought as its evolved so..

 

lol @ hearsay bullshit.

"One of my brother's father cousin cousin saw Bigfoot, and it's true so you can't disprove it."

 

The notion that .999 repeating equals 1 is just a mathematical convention to keep people from pointlessly bickering over an undefinable, infinitesimal difference.

 

been thinking again

1n = 0.99... is not true (you can read this n = 0.9....as well)

1n = 0.9... + 10 to the power of -infinity seems to be the term.

i started writing to a science site and had this revelation

n = 0.999... is incorrect, garbage in garbage out.

will keep you posted on the results from the scince site.