Topic awaiting preservation: The Greatest Above All? Or not? (Page 3 of 3)

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9X = (10-1)X not 9X = 10X - X

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Both of the above statements are legal, and they mean exactly the same...

I had some trouble accepting that 0.999(rep)=1 in the beginning, but both of the proofs offered for are valid as far as I can see and locigaly it is almost ok as well. The difference between .9999(rep) and 1 will approach 0 as the number of decimals goes towards infinity. So after an infinity number of decimals the difference should be 0, eg 0.999(rep)=1. Only problem now is seeing how this fits in fit the 'algebra's fundamental law' (or something like that) which states that in between any given two numbers there is an infinite of other numbers. So even if the difference between .999(rep) and 1 goes towards 0 after an infinite number of decimals there will always be an infinite other numbers between 0.999(rep) and 1 as long as the difference is greater than 0...

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

So then, by this reasoning anything that ends in .99999(rep) actually doesn't?

5.9999.... is really 6.

0.599999.... is really 0.6?

And, just going from what you said, Raptor... 0.9999(rep) doesn't exist... therefore it equals 1?

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More simply, how could you have a decimal, followed by an infinite number of zeros, ending with a one?

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Well. Why couldn't you? 1 - 0.99 = 0.01 does it not? Why shouldn't 1 - 0.999(rep) = 0.000(rep)1 Where the places after the decimal are equal? Since we're ceasing infinity to perform any sort of calculation at all you'll always get the afore-mentioned result. If .999(rep) is infinitely approaching 1 - Who decided that infinty ended and there was zero difference? Measurable or not, infinity determines that 0.9999(rep) != 1, by my understanding of its definition. As I said. Either it doesn't work, or it does and you don't believe in infinity. I'm trying to understand the meat behind why you believe that .9999(rep) = 1

Also... why does 10X - X != X +X +X +X +X +X +X +X +X?

I'm truly curious, I'm not trying to be difficult. I'm just looking for more... depth of reason to believe that .999(rep) = 1 until I'm out of reasons that it doesn't... I'll be skeptical. So please don't leave me floundering in the mathmatical quagmire.

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So then, by this reasoning anything that ends in .99999(rep) actually doesn't?

5.9999.... is really 6.

0.599999.... is really 0.6?

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Yes, Yes and Yes.

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Why shouldn't 1 - 0.999(rep) = 0.000(rep)1 Where the places after the decimal are equal?
Since we're ceasing infinity to perform any sort of calculation at all you'll always get the afore-mentioned result. If .999(rep) is infinitely approaching 1 - Who decided that infinty ended and there was zero difference?

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Damn, you got it backwards again. There IS zero difference BECAUSE infinity does NOT end. If 1 - 0.999 (rep) did not equal zero, YOU´d have to tell ME at which decimal place it would start differing from zero. And whatever your answer, it would be wrong, because we agreed above that there is an INFINITE number of zeroes before the one. And because infinity does NOT end, there is NO "one".

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Also... why does 10X - X != X +X +X +X +X +X +X +X +X?

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The point was that 10x -x indeed equals x+x+x+x+x+x+x+x+x and 0,999(rep) equals 1 for this very reason.

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I'm truly curious, I'm not trying to be difficult. I'm just looking for more... depth of reason to believe that .999(rep) = 1 until I'm out of reasons that it doesn't...

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You are. You just don´t notice.

Let me close with a quote that seems very appropriate here:

"In mathematics you don't understand things. You just get used to them."
-Johann von Neumann (1903 - 1957)

Hmmmm... I think I can accept that... That is a far better explaination then what I was able to find online.

I think I need to thump a few of my math teachers skulls.

Man, Pre-trig's hard enough without trying to convince people that 1=0.999(rep) but some how my science teacher convinced me that 100+10=100... Don't ask me how or why.

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"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
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some how my science teacher convinced me that 100+10=100... Don't ask me how or why.

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I promise we won´t ask, if you promise you´ll NEVER NEVER NEVER tell us, asked or not. Because I´m quite sure the explanation would make me bang my head against some more walls and I still got a headache from last time...

Well it had to do something like this... Sorry, just had to explain so you guys wouldn't think I'm a weirdo.

+100
10
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110

Right? No! How do we know what the hundredths digit on the ten number is? it may really be x10. So there fore we have to round to the nearest place value. 110 rounded equals 100. [Lets hope this formatting works ]

[Edit: looks like it didn't. Can't you under line using the <u> tag ('cept with brackets, not Greaterthen signs)]
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"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>



[This message has been edited by Ruku (edited 09-27-2003).]

I believe it's called accuracy. If I remember correctly, a line was put over a zero if it was accurate. Otherwise, a number was accurate only for the non-zero digits.

In the above example of 100 + 10, it would equal 110 if the tens is accurate in 100. But there is no line over the tens (I'm assuming the science teacher didn't have a line over his 100), so 100 is correct.

The general rule is to use the least amount of accuracy...?

Gremlin corection:

100 + 10 = 110
if the tens in 100 is accurate and the ones in 10 is accurate.

Googleplex^Googleplex

Now that is a big number!

Accuracy or not, it would be IDIOTIC to make your inaccuracy even bigger by ignoring the fact that you KNOW your result will be bigger (by 10, 11, or even 19) than the 100 (or 110, or 190) you started with.
In science what you do is find out (or estimate) how big your inaccuracy is and write it like this:

(150 +- 50) + (15 +- 5) = ( 165 +- sqrt(50^2 + 5^2) ) = ( 165 +- 50,25 )

And just so you don´t think now you understood it, here´s the whole story:
http://mathworld.wolfram.com/ErrorPropagation.html

BTW, as a tip for all of you, this site has everything you never wanted to know about maths and then some:
http://mathworld.wolfram.com/



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We hang the petty thieves and appoint the great ones to public office.
Aesop (620 BC - 560 BC)

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In science what you do is find out (or estimate) how big your inaccuracy is and write it like this:

(150 +- 50) + (15 +- 5) = ( 165 +- sqrt(50^2 + 5^2) ) = ( 165 +- 50,25 )

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But there are also a lot of places in science where you only give the answer in 'size', for example <some fancy equation> almost equal 10^16. It doesn't matter if it is 4.5*10^16 or 3.4*10^16. The answer is still right enough as long as the exponent is right.

There are also examples where you can say 'the number n in this equation is BIG, so we approximate to infinity'. It isn't unknown either to say 'this number is so small compared to this one, so might as well remove the small number at once and be done with it'.

And to keep the whole thing going there are many places in science where they 'overlook' answers to equations since they don't fit the theory, or that they allready found an answer that works.

So the accuracy in numbers used in science can vary a lot, but somehow they make it all work anyway

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

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But there are also a lot of places in science where you only give the answer in 'size', for example <some fancy equation> almost equal 10^16. It doesn't matter if it is 4.5*10^16 or 3.4*10^16. The answer is still right enough as long as the exponent is right.

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This is only done for when you just need a very rough estimate, or when your data is too unprecise to make a better statement. If you are going to do further calculations with your result, you better make it as precise as you can, and, even more important, give a good estimate of the error, because that allows you to judge the significance of your result.

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There are also examples where you can say 'the number n in this equation is BIG, so we approximate to infinity'. It isn't unknown either to say 'this number is so small compared to this one, so might as well remove the small number at once and be done with it'.

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That´s right. It´s done all the time, and that´s one of the cases where you only calculate the exponents, to see which numbers are so small you can kick them out of the calculation. In my above example the uncertainity of the 15 would have been ignored, for example, as it only contributes 1% to the error. But you usually wouldn´t ignore adding 10% to the result itself, by totally ignoring the 15.

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And to keep the whole thing going there are many places in science where they 'overlook' answers to equations since they don't fit the theory, or that they allready found an answer that works.

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I´m shure this happens all the time, too, although it shouldn´t. Or maybe it should, because when your result is significantly different from what you expect, the probability that you made a mistake is a lot higher than having discovered a new law of nature.

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We hang the petty thieves and appoint the great ones to public office.
Aesop (620 BC - 560 BC)

[This message has been edited by MW (edited 09-29-2003).]

Oh, BTW,

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to keep the whole thing going

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NOOOOOOOOOOOOO!!!!!!

Well I'm sure you all are glad that you have reached ultimate peace and obtained a higher level... this is about to reach 100 posts... As am I... Gotta do a sig for that >.> Big number for me ^^

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"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>