.999999 ......

[warf]

On another board, I was reading a thread about .99BAR, that is .9999 with an infinite number of 9s.

It is interesting because .99 BAR = 1.

Anyone ever study calculus and remember this?

[Dataspel]

Google reveals several proofs, for example check wiki:
http://en.wikipedia.org/wiki/Proof_that ... ._equals_1

The idea is that when we say the word equals, we have an
intuitive understanding that it means that two things are
identical. But 1 is a natural number and .9 BAR is a series,
that is a summation of a sequence. In this case, the word
equals is understood to mean: The series converges to
the specified numeric value as the summation sequence
approaches infinity.

Using the math interpretation, we can prove that .9 BAR equals 1.
But using the common definition of the word, we have to
say that it does not equal 1, it merely converges on 1 but never
quite reaches it.

[Buzzed]

Google reveals several proofs, for example check wiki:
http://en.wikipedia.org/wiki/Proof_that ... ._equals_1

The idea is that when we say the word equals, we have an
intuitive understanding that it means that two things are
identical. But 1 is a natural number and .9 BAR is a series,
that is a summation of a sequence. In this case, the word
equals is understood to mean: The series converges to
the specified numeric value as the summation sequence
approaches infinity.

Using the math interpretation, we can prove that .9 BAR equals 1.
But using the common definition of the word, we have to
say that it does not equal 1, it merely converges on 1 but never
quite reaches it.

Whatever! (said in a female teen voice)

[D.A.R.K.[CotC]]

That is corect

[TooLBlue]

On another board, I was reading a thread about .99BAR, that is .9999 with an infinite number of 9s.

It is interesting because .99 BAR = 1.

Anyone ever study calculus and remember this?

It was at that point in the class I started making paper airplanes and throwing them when the teacher's back was turned. I was typically considered the most well-behaved person in class, so you can imagine how much worse everybody else was after that

[warf]

I think the easiest wayto picture it is that 1/3 = .3Bar

3 * 1/3 = 1

and 3 * .3 bar = .9bar

Therfore .9 bar =1

Bueller?

[Serpent]

I think the easiest wayto picture it is that 1/3 = .3Bar

3 * 1/3 = 1

and 3 * .3 bar = .9bar

Therfore .9 bar =1

Bueller?

i caught it the first time you said it.... dont know what their problems were... .... never saw it written as bar though....just the line above the repeating number. hehe

[warf]

Google reveals several proofs, for example check wiki:
http://en.wikipedia.org/wiki/Proof_that ... ._equals_1

The idea is that when we say the word equals, we have an
intuitive understanding that it means that two things are
identical. But 1 is a natural number and .9 BAR is a series,
that is a summation of a sequence. In this case, the word
equals is understood to mean: The series converges to
the specified numeric value as the summation sequence
approaches infinity.

Using the math interpretation, we can prove that .9 BAR equals 1.
But using the common definition of the word, we have to
say that it does not equal 1, it merely converges on 1 but never
quite reaches it.

Based on the Wik entries, I would have to say .9bar = 1

Think this
1/9 = .1bar
2/9 = .2 bar
3/9=.3 bar
<snip>

8/9 = .8bar
9/9 = 1 or .9 Bar

I think it is a limitation of base 10

[D.A.R.K.[CotC]]

It's one of those infinity problems of calculus, kind of like the phenomenon known as "Gabriel's Horn". Any of you heard of it? Here's a simple explanation of what this "horn" is.

Imagine a cone, like an ice-cream cone. The phenomenon of Gabriel's Horn, proven by calculus level mathematics (we did a project on this nightmare), is that this object has a definite volume, but an infinite surface area: in lamens terms, if you were to fill the cone with paint there is a definite ammount of paint you can fill it with, but there is no ammount of paint that can cover the entire surface (inside or outside) of the cone with the paint. Kind of odd... But this is in theory, we can't make a "real one".

This is kind of related to what you're talking about b/c the equation for this object is 1/x which is similar because when X gets bigger, you get 0.0000000000000.......1, which in calculus, as x approaches infinity, the equation converges to 0, and yet not really. GOTTA LOVE MATH!!!

[warf]

It's one of those infinity problems of calculus, kind of like the phenomenon known as "Gabriel's Horn". Any of you heard of it? Here's a simple explanation of what this "horn" is.

Imagine a cone, like an ice-cream cone. The phenomenon of Gabriel's Horn, proven by calculus level mathematics (we did a project on this nightmare), is that this object has a definite volume, but an infinite surface area: in lamens terms, if you were to fill the cone with paint there is a definite ammount of paint you can fill it with, but there is no ammount of paint that can cover the entire surface (inside or outside) of the cone with the paint. Kind of odd... But this is in theory, we can't make a "real one".

This is kind of related to what you're talking about b/c the equation for this object is 1/x which is similar because when X gets bigger, you get 0.0000000000000.......1, which in calculus, as x approaches infinity, the equation converges to 0, and yet not really. GOTTA LOVE MATH!!!

Epsilon!

I took Real Variables in college. I pleaded with the instructor to give me an Epsilon, not fail me. Hardest class I ever took in college.

Much harder than Complex Variables or Diff-eq.

All that calculus, and I never ever use it. Ogh well, it is good for logic and problem solving.

[Baron[CotC]]

i caught it the first time you said it.... dont know what their problems were... .... never saw it written as bar though....just the line above the repeating number. hehe

Its difficult to get the computer to display the line above a number -- A lot of math symbols are difficult on a computer heh, so theyve come up with computer shorthands.