Simple mathematical problem (?)

Do we really have an agreement here?:jaw:
 
Congratulations to 69dodge.

:clap: :clap: :clap: :clap:

"Don Pardo, what prize do we have for our lucky winner?"
 
xouper said:
I propose we chalk it up to a misunderstanding of terminology and I take back all the mean things I said about you. :)
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no problem :D

Sorry for pissing you off:D
 
Excellent!

Now I am going to go out and see if I can't make tend to zero the rate at which my car leaks power steering fluid.

:D
 
Hey Walter,

What were you using to get the subsets in your post? I tried to cut n paste from maythtype but iy didn't work.
 
LuxFerum: Sorry for pissing you off:D
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Since I seem to be the only one who got pissed off and everyone else kept their cool, the problem is obviously not your fault. In fact, looking back at my participation in this thread, I'm inspired that others were able to remain civil and it's obviously something I need to work on.

[Quick, someone tell DiamondPoint what an ass I've sometimes been in this thread so he can lord it over me for the next six months.] :p
 
TillEulenspiegel said:
Hey Walter,

What were you using to get the subsets in your post? I tried to cut n paste from maythtype but iy didn't work.
Click to expand...
subscripts t<sub>i</sub> yields t<sub>i</sub>
superscripts t<sup>i</sup> yields t<sup>i</sup>

Also, if you see someone doing something you want to imitate, the most reliable method is to hit the quote button, and see how they did it in there post.

xouper posted about this somewhere in the Forum Help section I think, but I'm to lazy to find it.

Walt
 
Earthborn said:
Think of it this way:

What is the difference between 1 and 0.999(recurring)? The difference is infinitely close to 0, or in other words, the two are indistinguishable.

If 0.999(recurring) isn't 1 what on earth could it be? Is there a difference?
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There's a difference, it's just infinitely small.

Does it matter? Will it change anything? No, but it's still different.

Anyway, having 9.999...... In actual things is impossible, as you can't get infinitely small.
 
sorgoth: There's a difference, it's just infinitely small. Does it matter? Will it change anything? No, but it's still different. Anyway, having 9.999...... In actual things is impossible, as you can't get infinitely small.
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:hit: Here we go again. :rolleyes:
 
Walter Wayne said:
subscripts t<sub>i</sub> yields t<sub>i</sub>
superscripts t<sup>i</sup> yields t<sup>i</sup>t
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How did you get the code to appear instead of performing its function?

BillyJoe. :cool:
(Only joking, I hit the quote button like you said)
 
Walter Wayne said:

subscripts t<sub>i</sub> yields t<sub>i</sub>
superscripts t<sup>i</sup> yields t<sup>i</sup>

Also, if you see someone doing something you want to imitate, the most reliable method is to hit the quote button, and see how they did it in there post.

xouper posted about this somewhere in the Forum Help section I think, but I'm to lazy to find it.

Walt
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Ahhh so you have to use the BBS script and not a native application?
 
aerosolben said:
Don't you see the flaw in your reasoning? This would mean that there's a number larger than infinity, which is impossible by definition. Therefore, you cannot treat infinity the way you have been treating it. You must treat it as a limit to think of it infinitely rather than finitely.

Example: If we define a > 0 such that

a = 1 - 0.9~ (infinity nines)

we can also define b such that:

b = a/10 = 1 - 0.9~ (infinity+1 nines)

But infinity+1 does not exist! This is completely impossible! Therefore, a cannot be greater than 0; the only possible value for a is 0, such that a = b.
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WHAT flaw in my reasoning? I have shown that there are indeed an infinite number of points that are NEAR unity that are precisely NOT unity. That for any arbitrary point near one, there is one nearer. One of these points is 0.9~ (as we describe it in the decimal system). A "closer" one would probably be 0.F~16.

Interestingly, this type of mathematics has much to do with things like Mandelbrot and Julia sets - strange attractors. It's quite an interesting subject, really!
 
I think the problem of that notation is that it mixes the process with the limit.
Basicaly like this.

Code: 
      not there yet
             |
             | not there yet  
             | |
             | |     
           0,999...---Look the 3 little dots, we are there now, forget what we said before.
              |
              |
              |
            Still
             not
            there
 
Zep, didn't you read what 69dodge had to say about it, that the notation 0.999... is the limit of the infinite sequence of partial sums? Didn't you read the nice explanation I posted for you (in color, no less) about the difference between a sequence and a series, and that the infinite series is the limit of the infinite sequence of partial sums?

Zep: I have shown that there are indeed an infinite number of points that are NEAR unity that are precisely NOT unity. That for any arbitrary point near one, there is one nearer.
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Agreed. That's true of any real number.

One of these points is 0.9~ (as we describe it in the decimal system).
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You haven't shown that 0.999... is not equal to one.

Alternate question - Describe for us, in decimal notation, the number you would add to 0.999... to make the sum equal one. We are asking for a real number here, expressed in decimal notation.

A "closer" one would probably be 0.F~16.
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Wrong. The hexadecimal number 0.FFF... is exactly equal to the decimal number 0.999...

In fact, for any integer base B greater than one, where X=B-1, then 0.XXX... is also exactly equal to decimal number 0.999...

This is easy to prove formally and rigorously with the geometric series theorem. Give it a try.

What will it take for you agree that 0.999... is equal to one? What missing piece of understanding will cause a light to click on in your brain like it did with LuxFerum? Why do you continue to think you are right and that mathematicians have all lost their marbles?

As you know, 0.999... is a rational number, which means it can be represented by the ratio of two positive integers A and B. If you still think 0.999... is not equal to one, then show us that A is not equal to B. I'm saying it can't be done.
 
LuxFerum said:
I think the problem of that notation is that it mixes the process with the limit.
Basicaly like this.

Code: 
      not there yet
             |
             | not there yet  
             | |
             | |     
           0,999...---Look the 3 little dots, we are there now, forget what we said before.
              |
              |
              |
            Still
             not
            there
Click to expand...
Perhaps the solution is to read the number from right to left then? :)

[edit to add: Seriously Lux, when you see an ordinary number, like 0.428, do you think, "four tenths, no wait.. forty-two hundredths, hang on... four hundred and twenty eight thousandths" ?]
 
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