1 = .999?

[manikyath]

exactly, in math 0.9 recurring is never 1. Only using calculus we can imply that it is in some cases. And we can only do that because we understand that 0.9 recurring is incredibly close to 1.

and you blew way past the point again...

[Nineshadow]

it's not? 

Why not?

[mikat]

This is the video:

i JUST finished watching that video

(b4 u posted it)

[ZetZet]

and you blew way past the point again...

no I didn't you said the exact same thing I said. We can only assume/imply that it's infinitely close to 1 and then take it as equal in our assumption to use on calculations.

[ALwin]

my flaw was that I set n = .5 in the first line and n = .95 on the second line, notice how 10 x n (.5) does not equal anywhere close to 9.5

 

Yep I forgot to mention that part too.

[manikyath]

no I didn't you said the exact same thing I said. We can only assume/imply that it's infinitely close to 1 and then take it as equal in our assumption to use on calculations.

the thing is we dont assume, we use math to re-work problems to a point where we can press "equals" to prove our statement.

 

and the most interesting bit is that in examples like the 1+2+3+... problem, however unlikely the -1/12 result is to our human brians, it is actually used in science, and it actually works.

[Virtual01]

ITT: People debate facts and don't understand infinity

[Elehat]

nvm, it actually works with 0.5555, you just did it wrong. 

 

 

 

 

well no it's not. it's because 0.999 is THE exception. http://mathyquirks.blogspot.lt/2011/08/are-all-repeating-decimals-fractions-or.html

Actually any repeating decimal is rational (and therefore can by definition be represented as a fraction). Interestingly, if instead of decimals we used a continued fractions system, then every rational number would have a finite expression, and many irrational numbers would have repeating expressions. for example, the continued fraction for any nested radical (or indeed any algebraic number) would have a repeating expression, and even nasty trascendental numbers would have some nice features, for example, e expressed as a continued fraction is 2,1,2,1,1,4,1,1,6,1,1,8,1,1,10,... nice.

[1_thing]

Does 1 = .999?

 

 

Also if its called 0.999(repeating) then why isnt 1 called 0.999?

x=0.9999999.....

10x=9.9999999.....

9x=9

x=1

 

also its much easier to write 1 instead of 0.99999...

 

thing

[DebatED Nothing]

0.9 recurring is equal to one. Saying it's not is like saying that 0.3 recurring isn't a third, because no matter how many decimal places you do it to it will always be slightly less than a third. Yes, that is true, but we're talking about infinity here, so you can't use the "no matter how many..." argument, because we never stop at any decimal place.

Also, this is a pretty good demonstration of why 0.9 recurring = 1:

x=0.9999999.....

10x=9.9999999.....

9x=9

x=1

[babadoctor]

heh heh heh

[Kalle Hänninen]

no I didn't you said the exact same thing I said. We can only assume/imply that it's infinitely close to 1 and then take it as equal in our assumption to use on calculations.

0.999... Is rational number and rational numbers can be expressed as fractions, so what's the closest fraction of 1, if not 1?

[babadoctor]

999/1000 is 0.999 as a fraction.  You'd have to add to hit that 1000/1000, or do some really funky reflections that make no sense.  Otherwise, it's just rounding.  You'd hit 2 before you hit 1.

you would never reach 2.

or 1 for that matter

[Kalle Hänninen]

999/1000 is 0.999 as a fraction.  You'd have to add to hit that 1000/1000, or do some really funky reflections that make no sense.  Otherwise, it's just rounding.  You'd hit 2 before you hit 1.

NO. The sequence of nines continue to infinity, so no rational number other than one fit, when functions do not count as numbers. So 1-x isn't a number.

[KemoKa]

Nope, it isn't. 10 divided by three equals an irrational number the entirety of which no device can express.

 

.99999999999999 recurring is not 10. However, if you add enough to make it an even ten, then you would be adding

0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000..........

 

You'll never reach 00000000000000001. Never. And the difference is so insignificant that for all intents and purposes it doesn't exist and has never existed. it may as well be zero. If at some point the number ends, then you can solve for it. There's no problem. It's a quantifiable amount. If it's an irrational number made up solely of zeroes, then the one at the end doesn't exist. But it must! But it doesn't.
 

This is where mathematics and philosophy collide, this is a problem that human nature will never get over because our brains are wired to complete stuff. we're completionists.

But it will never be solved. Deal with it. And be happy about dealing with it, because at the end of the day...

It doesn't really matter that much!

[babadoctor]

If you triple the 2/3 aka 2/3*3/1 you'd get 2.  But, that would require some further math.    The point is that it would be easier to hit 2 since that only requires flipping 1/3 or some other fun stuff I don't have time to get into.  1 is far more difficult for it to equal due to the equality reason, so even if you were to say "1=0.999"  That would be rounding/estimates which is not true equality!  

ye

[babadoctor]

Nope, it isn't. 10 divided by three equals an irrational number the entirety of which no device can express.

 

.99999999999999 recurring is not 10. However, if you add enough to make it an even ten, then you would be adding

0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000..........

 

You'll never reach 00000000000000001. Never. And the difference is so insignificant that for all intents and purposes it doesn't exist and has never existed. it may as well be zero. If at some point the number ends, then you can solve for it. There's no problem. It's a quantifiable amount. If it's an irrational number made up solely of zeroes, then the one at the end doesn't exist. But it must! But it doesn't.

 

This is where mathematics and philosophy collide, this is a problem that human nature will never get over because our brains are wired to complete stuff. we're completionists.

But it will never be solved. Deal with it. And be happy about dealing with it, because at the end of the day...

It doesn't really matter that much!

YOU KNOW WHAT

MY BRAIN CANT FUNCTION THIS MATH

BRAIN EXPLODE!!!!

[Kalle Hänninen]

Which further brings in the equality rule.  If the 9s continued then the dominator would be however far we get with the continuation.  The numerator would just be more 9s.  So, that just further proves that it can't = 1.

I don't have time for this bullshit.

[babadoctor]

I don't have time for this bullshit.

oshit

we made him mad

[LukaP]

0.999... will never equal 1, only if you start rounding it off a bit... You'll ge very close to one but you'll never reach it. The most recent video from vsauce explains a similar thing.

nope. by definition 0.9999 periodic equals 1. here is the proof

 

0.9999*10 = 9.9999999 (all of this periodic)

9.9999-0.9999 = 9 = 9*0.9999 = 9*1 (per above) ergo

0.9999 = 1

[LukaP]

Nor, do I.  My point was simply that it would never equal 1, but how you could do some math that doesn't work to try and get another number.  I do know the math as I am in higher college Math classes, and there are actual theories of how it could though I don't support them as the math doesn't make sense.

Umm youre not in high enough math it seems. below i have an algebraic proof of it equaling 1, you could also do an analytical with a series of fractions and its limit towards infinity to prove it

 

nope. by definition 0.9999 periodic equals 1. here is the proof

 

0.9999*10 = 9.9999999 (all of this periodic)

9.9999-0.9999 = 9 = 9*0.9999 = 9*1 (per above) ergo

0.9999 = 1

[LukaP]

I'm actually in calculus and physics.  Now, look at my avatar of the Great Washu only then you will get my posts.

well then my homework for you, find a series i described, and calculate its limit as n approaches infinity

[ZetZet]

nope. by definition 0.9999 periodic equals 1. here is the proof

 

0.9999*10 = 9.9999999 (all of this periodic)

9.9999-0.9999 = 9 = 9*0.9999 = 9*1 (per above) ergo

0.9999 = 1

what..? 9*0.09999 is not 9 and it's definitely not 9*1

 

 

0.9999 cant be 1 and there is no proof that is it. whatever you can make up in two second just doesn't work because many people worked on this before you.

[ZetZet]

There are a few different ways 0.999 can equal one.  Geometric series, and another involves long division.

it's still not actually equaling one

[Sauron]

yes, 1 = 0.9 recurring. It's perfectly provable.

1/9 = 0.1 recurring.

1/9*9 = 1.

0.1recurring*9 = 0.9recurring = 1.

Those who deny it don't understand math.