0.99999999.......

[So the Heroes Fall]

Yes. People who say no are mostly uneducateds who ignore the math involved and just argue it doesn't "feel right". The math involved is pretty straightforward.

[Χahar]

Yes, but voted no in response to the original question.

[Fmr. Emperor PiT]

     Yes. As BRTD said, the math behind it is pretty clear-cut.

[A18]

Only if one assumes that 9.99999... refers to a real number, no?

[Swing low, sweet chariot. Comin' for to carry me home.]

Yes. People who say no are mostly uneducateds who ignore the math involved and just argue it doesn't "feel right". The math involved is pretty straightforward.

I see you have been peeking in my son's 6th grade math book.

[Vepres]

Sure, technically, but as it's impossible to imagine infinity, it is counter intuitive.

[Swing low, sweet chariot. Comin' for to carry me home.]

Yes. People who say no are mostly uneducateds who ignore the math involved and just argue it doesn't "feel right". The math involved is pretty straightforward.

also, in the real world of business (e.g. floating point computations), attempting to apply simple rules of algebra will lead to the wrong answer.  Example:

x(a+b) = xa + xb in your classroom, but in the world of computer calculations, this does NOT hold true.  In fact, in the world floating points, it rarely holds true.

[Senator Libertas]

This is religion and philosophy? Mathematics is not a religion, but I'm sure everyone is impressed at what you learned in school today.

[ChrisJG777]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

[I left.]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

[ChrisJG777]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

[I left.]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it?

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis

[ChrisJG777]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it?

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis

Still, 0.9999999... is not equal to 1. 

[I left.]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it?

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis

Still, 0.9999999... is not equal to 1. 

It is though

What's the difference between 0.9 and 1?
What's the difference between 0.99 and 1?
What's the difference between 0.999999999999 and 1?

If you truly assume an infinite number of 9s behind the decimal point....there can't be any difference between the two numbers.

To claim that the two numbers are not equal, you would have to assume a finite number of 9s behind the decimal point. But even 0.99999999999999999999999999999999999999999999 (and a million more 9s) is not equal to "0.99....".

[Swing low, sweet chariot. Comin' for to carry me home.]

Yes. People who say no are mostly uneducateds who ignore the math involved and just argue it doesn't "feel right". The math involved is pretty straightforward.

also, in the real world of business (e.g. floating point computations), attempting to apply simple rules of algebra will lead to the wrong answer.  Example:

x(a+b) = xa + xb in your classroom, but in the world of computer calculations, this does NOT hold true.  In fact, in the world floating points, it rarely holds true.

if you're interested, here is a quick overview of the why simple math principles fall apart when coded in floating point calculations:

http://www.cs.fsu.edu/~engelen/courses/HPC-adv/FP.pdf

[Senator Libertas]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it?

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis

Still, 0.9999999... is not equal to 1. 

(1/3)=0.333333333....

(2/3)=0.666666666....

(3/3)=0.999999999....


Gotta wonder whether that excellent public school education you kept telling me about is to blame for an 18-year-old being ignorant of a basic mathematical fact...

[dialectical fetishist]

I was always taught to regard it as 1.

[Sibboleth]

numbers.

do. not. like.

do. no. want.

go away. numbers.

[Fmr. Emperor PiT]

It's certainly very close to 1, and if I was using it in some mathematical equation and didn't need to be too precise, I'd put it down as 1, but in the end though 0.9999999... ≈ 1, at the same time 0.9999999... ≠ 1 either.

It's infinitely close to 1, however, making it mathematically equal.

Quite frankly I fail to see how it's equal to 1, indeed it's very close, but just by looking at it you can see that it's not exactly equal.

Fun isn't it?

f(x) = 1 / x², a lot of people would say, never touches the x-axis, but only gets closer and closer to it.

It does, though, in theory. Under the same principle as the original question here, the function is considered to be infinitely long, and thus it also becomes infinitely close to the x-axis

     It all goes back to Zeno's paradox, really. Achilles races with a tortoise. Achilles starts at point A while the tortoise starts at a point B further ahead. By the time he reaches point B, the tortoise has reached point C. By the time Achilles reaches point C, the tortoise has reached point D, & so forth. The implication is that Achilles never reaches the tortoise, but we know that would be false. As such, we realize that at x=infinity, the graph of f(x) = 1/x² does in fact equal 0. I find limits to be rather fascinating, really.

[So the Heroes Fall]

What does 1-0.999999.... equal if not zero?

You can't say a number with an infinite number of zeroes between the decimal point and a one, because infinite means without end. So nothing can come after the zeroes.

[Aizen]

nope. i once did this on a math quiz. if the answer was 28 i would put 27.999999~ and i got it wrong. since i got it wrong and failed the math quiz because i made all my answers like that, it must not be true.

[Californian Tony]

0.9=1

I assumed that was the meaning of the question.

[dialectical fetishist]

0.9=1

I assumed that was the meaning of the question.

The meaning was 0.9999999∞ being the same as 1, which it is for all purposes, given that it is just 0.000000....1 from it.

[muon2]

One area of discrepancy is that the symbol "1" can be used in different contexts. jmfcst's example of its use in floating point arithmetic is one such example. But even in abstract mathematics it can have different meanings.

As a real number the symbol 1 refers to the number that can be represented by any convergent sequence that becomes arbitrarily close to that specified value. Decimal numbers are one form of describing a convergent sequence of a sum of fractions:

1.000... = 1/1 + 0/10 + 0/100 + 0/1000 + ...
0.999... = 0/1 + 9/10 + 9/100 + 9/1000 + ...

Since these sequential sums converge to the same value they represent the same real number. Other sequential sums also represent the real number 1:

1/2 + 1/4 + 1/8 + 1/16 + ...
4/5 + 4/25 + 4/125 + 4/625 + ...

And all these sequences are equal as real numbers.

However, the symbol 1 can also refer to the integer 1, which it might be if use for instance as the simplest counting number. In that case decimal or other fractional sequences can not equate to 1, since they are not themselves only integers. The statement 1 (integer) = 0.999... (real) is either confusing or meaningless since the two sides of the equation are different entities.

When a question like the one for this thread is posted, I assume that the questioner intends for the equals sign to be sensible and relate two items of the same sort. Therefore I answered yes, but I recognize that there is ambiguity in the use of the symbol 1.

[titaniumtux]

(3/3)=0.999999999....

Epic math fail. Three divided by three is one. Ridiculous to suggest that three thirds is anything but one...srsly...