0.9999.... is equal to 1

I honestly thought that by this time, everyone in the world knew this was true, save those who have absolutely no idea what numbers are.....ok, I'll do my best to explain this to all you would-be trolls.

1/3 = 0.333
now multiply both sides by 3 and you get:
3/3 = 0.9999....
OR
1 = 0.9999....

Now, Let's start with 1 = 0.99999.... this time.
Subtract 0.9999.... from each side and you get:
0 = 0.00000....
Yes, there is a 1 there, but it is exactly aleph null zeros from the decimal.....meaning it kinda isn't there, and that you just subtracted the same number from two numbers and got the same answer for both....thus they must be equal.

Last: between any two unequal real numbers, there are infinitely many numbers. I'd like to challenge anyone to find a number between 0.9999..... and 1. If you can find that number, then you win infinitely many internets, but if not, just admit that 0.999... does, in fact, equal 1.

Making such a thread automatically makes you a troll.  Instead of keeping the cancer in one thread, you helped it spread.  Good job.

>>1
are you doing arithmetic with numbers, or with symbols that you believe to be numbers?  I say it is a parlor trick.

>>3
These are numbers, and every procedure is algebraically correct. No tricks, no ones up my sleeve.....

>>2
You've made no contribution to the topic at hand, and actually have tried to change the topic. Submit something more thoughtful and I'll consider considering it.

What is 1 over .999R to infinity?

>>1
YHBT. Quit being part of the cancer.

>>4
I'm not changing the subject, just pointing out your phail.

A number that is between .999... and 1?

1 - .00...1

>>8
.00...1 isn't a number that makes sense. It's a meaningless combination of symbols.

.000...1 is hardly a meaningless combinations of symbols.  It's clearly the limit of the sequence An = 10^(-n). Which is zero.  So .000...1 = 0.

>>10
It is meaningless because there can be no last digit in an infinite series. In .00...1 you have an infinite number of zeros, and a last digit 1. It's nonsensical.

So, what is

1
_
.999Rinfinity?

>>12
LaTeX failure.
Or is that not the answer you had in mind?

I meant 1 divided by .999Rinfinity.  I was wondering what the answer was without resorting to rounding up.

>>14
The answer is 1. There is no rounding up since 1 and .(9) are the same number. Not ``nearly'' the same number, but actually the very same.

>>15

Stop using your calculator.

if 1=(9) then 11=(99)

>>16,17
gb2 middle school

10 and 9 are the same number.

>>8
Assuming that 0.00...1 actually made sense, 1 - 0.0....1 would be the same as 0.999...

>>12
If 0.999.... is equal to 1, then it would be 1, if not, it would be 1.000.....1, another nonsensical number.

I think it would help a lot of people if they knew the properties of infinity. Let's say you have a line (or a ray, line segment, whatever you wanna call it), originating at one point and proceeding in one direction for an infinite distance (let's say aleph null distance). If you're standing at the origin, the end of this line wouldn't just be a very long distance away, because a "very long distance" suggests that if you go a very long time, you'll get there. You will never get to the end of this line, because it is never there. Now, let's replace the origin with 1. and the line with a string of zeros. At the "end" of this string of zeros is a one. The problem is, you can never get to that 1. If something can never be reached, has never really been seen, and who's position has been identified as being the same as an imaginary entity's position (the end of infinity), then is it truly there? I say no, the vast majority of the mathematical community says no, and you should say no.

>>20
who's
...

Just give up; you can't convince the trolls/fools.  The latter will never understand, and the former will never let you know that they understand.

No, this one is pretty easy to show...

x = 0.9999....
10x = 9.9999....

10x - x = 9x

9.9999.... - .9999...... = 9

9x = 9
 x = 1

Seems pretty obvious to me.

>1
This is a distortion created by our base-10 place-oriented numbering system.  If we had 9 toes and fingers, we'd be saying the same about 5 and possibly 2.

Let's try the same with a base-3 system instead.  Only symbols here are 0, 1, and 2, and the places are 1's, 3's, 9's, 27's, 81's, etc.  I will reinforce the base with angle brackets (i.e., 20<3> = 6<10>)

1<3> / 10<3> = 0.1<3>
2<3> / 10<3> = 0.2<3>
10<3> / 10<3> = 1.0<3>

Sorry, 1 does equal 1 after all.

You can't solve a problem until you use the right set of symbols first.

>>22
I think I see something here. Your proof is invalid in the manner you propose, sort of.

x=0.999...
10x=9.999....
Good so far.

10x-x=9x
Now what you've done is said:
10(0.999...)-0.9999=9(0.999....)
9.999...-0.999...=9(0.999....)
9=9(0.999...)
See the problem? This only holds true if 0.999... is equal to 1, and so uses circular argument. BUT...
If this doesn't hold true, then 10x-x=/=9x, and so violates a theorem. Thus, this proof would better be shown via reductio ad absurdum.

>>23
I honestly have no idea how this is relevant to the current topic. I've assumed the axiom that 1=1 in all bases throughout this entire post. I fully understand bases, but still, these base-3 fractions have nothing to do with 0.999.... in base ten. You may be looking for 0.222...., which I believe would be equal to 1 in base-3. Now, whether or not this misunderstanding is due to true irrelevance on your part or through a fault of mine, I can't determine.

>>24
It's relevant because base 10 is incapable of expressing 1/3 as a decimal, where base 3 is.  So the irregularity is an aberration caused by the symbol system used.  The number that the symbol represents is the same in either system.

The base-3 fractions have nothing to do with the base 10 numbers per se, but it illustrates that by using different bases, the problem doesn't exist.  Therefore the problem is with a specific base, i.e. base 10 and not more fundamental mathematical theories.

>>25
The only ``problem'' here is morons and trolls and idiots feeding them.

The Babylonians were right.  We should have just stuck with base 60 and everyone would be happy.

>>27
But then what is 0.(59) recurring?

>>28
not equal to 1

>>29

touche.

>>30
If by ``touche'' you mean ``wrong''.

>>19
10 and 9 are not the same number because there is at least one fractional value between them, such as 9.5. 1 and 0.999... are the same number because there is nothing between them. There is no such thing as 0.999...5. It is the same concept as colors: red and yellow are not the same color because there is something between them, namely orange. Red and yellow are just points on an analog spectrum.

>>29
Wrong (as already said).

Counting whole numbers in base10 works like this: (0)(0)(0), (0)(0)(1), (0)(0)(2), ... , (0)(0)(9), (0)(1)(0). There is an infinite series of 0's going off to the left, they just aren't mentioned for simplicity. A whole number is simply one with an infinite series of 0's that also goes off to the right of the radix point ("decimal point" in base10), which is likewise usually ignored.

Counting whole numbers in base60 would be: (0)(0)(0), (0)(0)(1), (0)(0)(2), (0)(0)(3), ... , (0)(0)(59), (0)(1)(0).

(0)(0).(59)(59)(59)... is the same as (0)(1).(0)(0)(0)..., which is simplified to 1 for convenience.

>>32
Eep.  You fucked up.  It is possible to have two different irrational numbers that do not have an intervening fraction, but that doesn't mean two different irrationals are equal.

>>33
Proof or GTFO.

>>32 their diferent.
Take the difference.
1 - 0.(59)(59)(59)... = 0.00.........1
difference is positive, so their different numbers

>>35
Worthless pigfucker.

>>23
First interesting poast in this pile of phail.

However, it should be noted that the definition of a real number makes no reference to the base used.

what about base 7?