i saw an equation in my dreams lastnight! opinions?

[Ouroboros]

Where did you get the (3/10)/(1-1/10) from?

Converging geometric series.

Can't do his fancy math formulas, but basically you can simplify series of different kinds.

Gauss was the first one to figure that one out, if I'm not mistaken.

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Arithmetic and Geometric Series (Progressions

 

[Curious George]

Converging geometric series.

Can't do his fancy math formulas, but basically you can simplify series of different kinds.

Gauss was the first one to figure that one out, if I'm not mistaken.

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Arithmetic and Geometric Series (Progressions

I think he was pointing out that you have to use limits to get that convergence

 

[Enai de a lukal]

How did this thread turn in yet another thread about the fact that .999...=1? Actually, don't answer that.

 

[LegionOnomaMoi]

Where did you get the (3/10)/(1-1/10) from?

It's a geometric series. For any number r with an absolute value less than one, with r being the ratio between terms of a geometric sequence, the formula that in this case is the fractional expression used holds. To get the generic formula, simply use the first term as the numerator and 1 - r as the denominator. Then sum the term according to the rule Sum(r^n) from the first term to infinity. The series converges.

 

[Curious George]

It's a geometric series. For any number r with an absolute value less than one, with r being the ratio between terms of a geometric sequence, the formula that in this case is the fractional expression used holds. To get the generic formula, simply use the first term as the numerator and 1 - r as the denominator. Then sum the term according to the rule Sum(r^n) from the first term to infinity. The series converges.

Which is a limit. 1-r^n as n -> infinity=1 when |r|<1. Is a limit. This is why we use the first term in the numerator.

 

[LegionOnomaMoi]

Which is a limit. 1-r^n as n -> infinity=1 when |r|<1. Is a limit.

Of course. However, this formula itself does not. I actually edited the post as originally I only had 1 = [the formula in this case]. But I still mean to use one of the methods to construct the reals when I can figure out what is the one that most closely resembles the original formulation. So I decided not to include the convergence proof required to show that the formula holds in this case and infinitely many more.

This is why we use the first term in the numerator.

It's the reason we can even have a formula that gives us the required number (not just in this case but in any other for r in the required interval) for an infinite series. But as this particular series need not be proved itself to be convergent given the value of the ratio, we don't actually have to use limits here. But we should certainly understand that if we did not have a proof that this series is convergent because r is in the appropriate interval, we would need to show whether it converges. That's why I said in my post that it doesn't involve limits directly.

 

[crossfire]

How did this thread turn in yet another thread about the fact that .999...=1? Actually, don't answer that.

Well, because in this thread, everything equals one!

 

[Ouroboros]

I think he was pointing out that you have to use limits to get that convergence

His post seemed to ask how Legion got from A to B. (I mentioned limits in an earlier post btw.)

Oh, and also, Legion used an infinite series not a limit. The sum of a series from n=0->&#8734; isn't the same as limit when n->&#8734;. Different functions would have to be used.

 

[LegionOnomaMoi]

I think he was pointing out that you have to use limits to get that convergence

You have to use limits for any convergence. To point this out is like saying you need addition to add. Hence your response, which was to point out that this still involves limits, and hence the statement in my original post that it does not directly involve limits. If it didn't involve limits at all, then this makes no sense. If it was unclear, why not ask or seek clarification the way you did? I thought that including an infinite series equal to a finite value would make it blatantly obvious that it involved limits even if it isn't necessary to use limits to get that particular expression. Apparently not. Eh. I've been mistaken before.

 

[sandy whitelinger]

I think he was pointing out that you have to use limits to get that convergence

I've reached my limit with this thread.

 

[Ouroboros]

I've reached my limit with this thread.

The limit is reached when .999... posts turns to 1.

.999... bottles of beer on the wall, .999... bottles of beer... no wait, that's not even one pint!

 

[Poeticus]

Where is the OP?

 

[Enai de a lukal]

Well, and we can't forget that- 1 is the loneliest number... And that 2... can be as bad as 1, and that its the loneliest number, since the number 1.

 

[Enai de a lukal]

Well, because in this thread, everything equals one!

So I hear.

 

[Willamena]

Well, because in this thread, everything equals one!

Everything does equal one, just not mathematically.

 

[Adjacent]

What the hell is this?50 x 0 is zero.If not,then you are free to create a new branch of logic .

 

[Gjallarhorn]

What the hell is this?50 x 0 is zero.If not,then you are free to create a new branch of logic .

Playing a little fast and loose there with the word "logic".

 

[Kilgore Trout]

Playing a little fast and loose there with the word "logic".

Yes, well this is RF.

 

[Ouroboros]

It's fuzzy.

 

[Monk Of Reason]

Playing a little fast and loose there with the word "logic".

One might make the argument that it would require a new system of logic to remain resonable to assume that 55 quantities of zero would be anything but still...zero.