0.9999999...=1.0

It's a fact. Deal with it, bitches.

>>117
U FAIL!

{0.000...1} =/= {1} - {0.999...}

The number {0.000...1} doesn't exist as an infinite expression.  The actual expression is {0.000...}, which converges to ZERO.  Hence, your stupid fucking formula should be:

{0.999...} + {0.000...} = {0.999...} + {0} = {1} + {0} = {1}

YOU ARE A STUPID FUCKER!  STUPID!  STUPID!  STUPID!

RedCream is obviously not familiar with the hyperreal number system! FAGGUT

>>121
You're wrong: 0.999...  == 1
              0.000...1 == 0,
           => 0.000...1 == 1 - 0.999....
  

what your doing is rounding up, otherwise no it doesnt come out to be one, its a decimal and stays as such
-but then again what would i know all i do is build cc's and repair battle crusiers for deep space flight, theres no mathematics in my job. 

0.000...1 denotes a finite (but unspecified) string of 0s followed by a 1.

e.g. 0.000....1 might mean 0.00000000000000000000001 or 0.0000000000000000000000000000000000000000000000001

funny to think that there is an actual proof out there for this...

i believe my proof is the best though :)

1/3 = .33333...
2/3 = .66666...
1/3 + 2/3 = .33333... + .66666...
.33333... + .66666... = .99999....
1/3 + 2/3 = 1
.99999 = 1

QED?

it only works if you accept the decimal representation of rational numbers as something acceptable to do arithmetic on when there is no last digit

>>127
You aren't doing arithmetic on the decimal representations.

>>128
you are if you are solving as shown in >>126

>>7

It is impossible for any particle to ACCELERATE to the speed of light. Einstein's theory doesn't say anything about particles already travelling at the speed of light.

>>130
that's the whole idea of infinite energy: you can't. Except for massless particles, which always travel at the speed of light.

What is with the hate? Calling those particles massless?

It does not equal 1, it gets infinitely close though.

0.999... is not a variable, it is fixed.  It cannot get infinitely close.  It is already infinitely close (i.e. any positive difference is greater than the actual difference => the difference is zero => they are the same) or it is not infinitely close (i.e. different so there is a number in between them).

hrm, if we're not being picky, why not say 1=2... I mean, it's pretty close...

fucktards...

>>134
worst troll ever.

>>135
NO U

>>136 sorry 136 it is you

>>100
Not a real GET, but close.

and so we have an example of Marshall Mcluhan's tetrad, whereby a medium "overheats", or reverses into an opposing form, when taken to its extreme

x=0,999...
10x = 10*0,999...=9,999...=9+0,999...=9+x
10x=9+x
9x=9
x=1
Find a fallacy - if you can't, then 0,999...=1

Also, ITT stupid people

>>141
i reported the fallacy earlier

>>142

If it was >>76 then yes, you can. Arithmetic isn't about working digit by digit. These are numbers, so we consider them as ideas, not physical, actual objects. Therefore, there is no "time" needed to do arithmetic. The equations exist per se - they can be proved true or false at any given moment. These ones are, by the elementary laws of arithmetics, true.

per se, more like per gay

>>141

replace x with 5 and do similar calculations, it will prove 5=1, I  shit you not... SO, IT MUST BE TRUE...

I think what one group of people is trying to get to is that 0.9999 (repeat infinitely) is for all intents and purposes 1...

that however does not mean that it equals 1.
You see, there's a little thing called the equals sign, or "="...
One of the first things you learn in math is that whatever is on  either side of the equals sign has to amount to *exactly* the same as on the other side, or the equation or whatever is just wrong. Plain wrong. Thus, any one single number cannot equal any other number than itself. 1=1... 1!=1.1... same idea...

Now, however, if you argue that because 0.999... is repeated infinitely and there by cannot be treated as a normal number but more like some sort of idea or concept, then yes that may be the case, but THEN you cannot equal a concept or an idea, something that is NOT a normal number, with something that IS a number... that would be like saying: cherry toppings=1...

but then again, this whole thread is just one big troll, but it's a fun troll...

No dumbass, it does equal one.

Also, you fail at arithmetic.

>>145 Could you please show us said calculations? Also, EVERY number is an idea ("normal" numbers too). What else could they be?

>>146
No, the idea of what 0.999... represents equals one, but the symbol 0.999... itself is pretty shit bad at equaling one.

x=0.9999999...
10x=9.999999...
10x-9=0.999999...
10x-9=x
9x=9
x=9/9
x=1

Also:
1/9=0.1111111...
9*(1/9)=9*0.111111111...
1=0.99999999...

Also, the sum to infinity of a sequence is: S=a/(1-r), where a is the first term and r is the common ratio:

Sequence is: 0.9+0.09+0.009...
a=0.9. r=0.1

S=0.9/(1-0.1)
S=0.9/0.9
S=1

Is three proofs enough?

>>149 That's true, but it's caused by imperfectness of the symbols we are using. The numbers in themselves are, as you said, equal.

the fact is that this 0.999... (or usually written 0.(9), or some other ways not possible on a keyboard) doesn't actually exist as a number... whenever 0.9 has few enough decimals not to be infinite, it does not equal 1... however, whenever it "steps over the infinite boundary" it is no longer 0.999, it is instead 1... same goes with 1.(1) (becomes 1.2) and any other number you can think of...

To 152:
x=1.1111111...
0.1x=0.11111...
0.1x=x-1
0.9x=1
x=10/9
x=1.111111...

So, 'fraid not. It would work with 1.1999999 though.

instead of trying to prove it using mathematical formulas, which may or may not be true  due to any number of factors in different scenarious, logically reason your way to a conclusion. Math is logical and can be proved logically very easily, but is harder to prove mathematically, because proving something "with itself" is like trying to say "that's the sun, because it's the sun".

It is the fact that when a number "crosses the border" between having a set number of decimals, i.e. being finite, and having an infinite number of decimals, it is no longer the beforementioned number, it instead "becomes" (or more accurately, it already is) the 'next' number in a 'logical series'.

Though truth to tell I am damn tired right now, and I can't really think straight. What I just said might not apply to series of decimals below .(5)... or maybe even below .(9)...

But I don't really care since this is just 4chan and you'll just troll anyway... so if someone wants to pick up where I left, go ahead.

>>154

People should shut the fuck up about maths if they don't know what they're talking about.

Real numbers, defined as limits of cauchy sequences. This has all been said before. 0.99999999....= 1.

It's not difficult.

>>151
In which case, let us never write the imperfect symbol 0.999... again.

>>155
Makes no difference to me if I reject the symbol 0.999... as being a limit.

Try Dedekind cuts, not limits of Cauchy seqences.

more like diddley cunts

FUUUUUCK!  Are you 'tards STILL "arguing" this?  Look it's SIMPLE:

"What is 5/9 expressed as a decimal?"

Once you answer that, you automatically know that 0.999... can be expressed as a ratio of two integers, which just happen to be 1/1.