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Old November 28th, 2012, 10:33 PM   #51 (permalink)
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Originally Posted by palmtree5 View Post
Never thought I'd see calculus references here...
I thought calculus was a robot in the cartoon "Futurama"?
oh wait that was calculon...sorry


This thread has gone clear over my noggin!
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Old November 29th, 2012, 02:16 AM   #52 (permalink)
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Part of your problem
Its not my problem. The problem was posted in post 1 by the OP.... In Base 10.
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Old November 29th, 2012, 04:24 AM   #53 (permalink)
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I think it's something like this.

0.9999... Isn't one, if it was one, it would be 1.

It is however a very close approximation of one.

It is not one simply because there is ALWAYS a remainder.

Add 0.0001 to 0.9999 and you get 1 just as if it were to any decimal point or infinity.

Factually, accurately 0.9999... Will never and can never be one it can only be approximated to be one. Imo.
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Old November 29th, 2012, 09:51 AM   #54 (permalink)
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Originally Posted by XplosiV View Post
I think it's something like this.

0.9999... Isn't one, if it was one, it would be 1.

It is however a very close approximation of one.

It is not one simply because there is ALWAYS a remainder.

Add 0.0001 to 0.9999 and you get 1 just as if it were to any decimal point or infinity.

Factually, accurately 0.9999... Will never and can never be one it can only be approximated to be one. Imo.
No, it is one. 0.999... is an infinite series, specifically a geometric series with r=1/10 and a=9, represented as jhawkkw posted in his handwritten proof. The sum of a geometric series with 0 < r < 1 is a/(1 - r). If you disregard the 0th term, as .9999...requires you to do (because it's .9999... not 9.9999...) , the series sums to a/(1-r) - a. Substitute the values in, 9/(1-(1/10) ) - 9 = 1.

If you haven't had calculus, you may not be able to come to grips with the fact that a sum of an infinite number of finite terms may in fact converge to a real, finite number. It's still true though.
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Old November 29th, 2012, 10:12 PM   #55 (permalink)
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It's really counter intuitive. Before having university classes on that matter, I didn't believe it either. But yeah, I still think that the best way to explain it (without it getting complicated) is this one:

1 = 1
(3/3) = 1
(1/3) + (1/3) + (1/3) = 1
0.3333... + 0.333... + 0.33333... = 1
0.9999... = 1


There's no approximation anywhere in there.
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Old November 30th, 2012, 06:00 AM   #56 (permalink)
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Nope. It's rubbish.
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Old December 1st, 2012, 01:21 PM   #57 (permalink)
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WOW . . I just discovered that .00001=.99999!

Amazing. Time to hit the college prep math books for a refresher.

Next thing you know, Three Dog Night will be sued for telling us that 'One is the Loneliest Integer' when the Internet will prove with unfailing logic that 4 is actually the loneliest integer.

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Originally Posted by DaSchmarotzer View Post
It's really counter intuitive. Before having university classes on that matter, I didn't believe it either. But yeah, I still think that the best way to explain it (without it getting complicated) is this one:

1 = 1
(3/3) = 1
(1/3) + (1/3) + (1/3) = 1
0.3333... + 0.333... + 0.33333... = 1
0.9999... = 1


There's no approximation anywhere in there.
So 1 is exactly equal to .9999? And .9999 is exactly the same as 1? What about .9? What is that equal to?

If I borrow a dollar from you and you really need to be paid back in full, can I settle the debt with 99 cents? Same as a dollar, right? If I brrow three or five or a grand, can I settle the debt in full by paying you just little less than I borrowed? Apparently I can. Will you be my next loan officer?

So, .9999 = 3/3 and 1/3+1/3+1/3=.9999?

And so forth?

Your mistake is in the 4th line: 0.3333... + 0.333... + 0.33333 = .9999 not one which is equal to .999994 x the Internet = Bollocks. Some of us seem to leave up the missing piece of the math. I'll call it B for Bollocks.

Therefore, .9999 (B) = 1

I do know that E-MC Squared is not true. E=MC Hammer and You Can't Touch That, my friend.
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Old December 1st, 2012, 01:42 PM   #58 (permalink)
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Originally Posted by Bob Maxey View Post
WOW . . I just discovered that .00001=.99999!

Amazing. Time to hit the college prep math books for a refresher.

Next thing you know, Three Dog Night will be sued for telling us that 'One is the Loneliest Integer' when the Internet will prove with unfailing logic that 4 is actually the loneliest integer.






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Originally Posted by Bob Maxey View Post
So 1 is exactly equal to .9999? And .9999 is exactly the same as 1? What about .9? What is that equal to?

If I borrow a dollar from you and you really need to be paid back in full, can I settle the debt with 99 cents? Same as a dollar, right? If I brrow three or five or a grand, can I settle the debt in full by paying you just little less than I borrowed? Apparently I can. Will you be my next loan officer?

So, .9999 = 3/3 and 1/3+1/3+1/3=.9999?

And so forth?

Your mistake is in the 4th line: 0.3333... + 0.333... + 0.33333 = .9999 not one which is equal to .999994 x the Internet = Bollocks. Some of us seem to leave up the missing piece of the math. I'll call it B for Bollocks.

Therefore, .9999 (B) = 1

I do know that E-MC Squared is not true. E=MC Hammer and You Can't Touch That, my friend.
Don't forget that the ellipses ("...") at the end of ".999..." are very important / significant.



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Old December 1st, 2012, 02:11 PM   #59 (permalink)
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Now that I know that less than one is equal to one, I am very concerned about the future of Ohms Law. Not Ohmslaw the delightful crunchy cabbage and apple salad, mind you. I almost cried when I discovered that Pluto is no longer a planet and nobody has figured out if it is possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions.

So as you might gather, I do not sleep much at night.

Apparently, these calculations will be on one or more of my upcoming tests:

P = E2/R, P = I2 * R, P = E * I, E = sqrt(P * R), E = P/I, E = I * R, I = E/R, I = P/E,
I = sqrt(P/R), R = E/I, R = E2/P and my personal favorite, R = P/I2

Please . . . will an expert confirm I can still use these simple formulas and get me my tickets if I substitute .9999 for 1? If it turns out that one amp is equal to less than one amp, my 10 mW Gunn diode and a mixer diode circuits could open a hole to the nexus of the cosmos if I am off by so much as .9999 somethings. And then where will I be? Lost in the nexus, so Bob needs help.

You do not screw around with microwaves, after all.

And if you are at sea and I my ship's radar settings are wrong, well, think back to Gilligan's island. You might be stuck with a few Gilligan's.

Or worse, remember Lost?

If i read on the net that Ohms Law is wrong, will my clock radio stop working? I think it will. Please save both the children and Ohms Law. If one is equal to less than one, it can have an effect on my studies for my Amateur Extra license test and eventually my GROL + Ship Radar Endorsement. Please contact my license examiner and let him or her know that the tests need to be changed.

My fear is we will learn that current through a conductor between two points is directly proportional to the potential difference across the two points is wrong, and I will not get up on time because my clock is no longer accurate. I might need a new clock radio with a digital dial. When I need to get up at 1 AM, I can set my clock to .9999. then it might work.

Less than one equals one. Pluto is no longer a planet, the world will end once again in 2012, Justin Bieber will keep recording, Lady Gaga will still be allowed to wear meat clothing and we will never know for certain if there is a finite upper bound on the multiplicities of the entries greater than 1 in Pascal's triangle.

I think I will end it all. Tomorrow after lunch, at .9999 O' Clock sharp. Give or take a minute or so. Rather, .9999 or .9997 or .9993.
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Old December 1st, 2012, 02:19 PM   #60 (permalink)
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okay guys, here's a video to settle it all!!!

9.999... reasons that .999... = 1 - YouTube
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Old December 1st, 2012, 02:21 PM   #61 (permalink)
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remember that 0.99999... repeating is NOT the same number as 0.9 or 0.99 or 0.999 or 0.9999999999999999999999999
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Old December 1st, 2012, 08:37 PM   #62 (permalink)
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remember that 0.99999... repeating is NOT the same number as 0.9 or 0.99 or 0.999 or 0.9999999999999999999999999
Exactly.

In this case 0.9999... meant that it was repeating to infinity. I thought it was pretty obvious from the posts before. Since when does (1/3) in decimal form not repeat to infinity?
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Old December 2nd, 2012, 04:08 AM   #63 (permalink)
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1 - 0.999999999..... = ??
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Old December 2nd, 2012, 08:51 PM   #64 (permalink)
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Originally Posted by jhawkkw View Post
That is one way to show repeating decimals, but the ellipses "..." is also widely accepted in mathematics to signify a repeating sequence.
The way I was taught mathematics and composition, an overline placed above the sequence is used to indicate a repeating sequence, and the ellipsis is used in composition (writing) to indicate that text has been skipped. An ellipsis can be used in mathematical notation for the same purpose as with composition, but isn't interchangeable with the overline. But because many websites and other Internet services don't offer the entire range of possible characters, substitutes for full mathematical notation are often used for convenience.

When it comes to decimal numbers like a string of nines to the right of the decimal, you can either round up to a solid 1 or accept that adding more nines will approach but never reach 1.
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Old December 2nd, 2012, 09:20 PM   #65 (permalink)
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Originally Posted by Speed Daemon View Post
The way I was taught mathematics and composition, an overline placed above the sequence is used to indicate a repeating sequence, and the ellipsis is used in composition (writing) to indicate that text has been skipped. An ellipsis can be used in mathematical notation for the same purpose as with composition, but isn't interchangeable with the overline. But because many websites and other Internet services don't offer the entire range of possible characters, substitutes for full mathematical notation are often used for convenience.

When it comes to decimal numbers like a string of nines to the right of the decimal, you can either round up to a solid 1 or accept that adding more nines will approach but never reach 1.
That is more or less correct regarding the ellipsis in mathematics. It is generally used to signify that a number or trend continues. If it terminates, the last term is written; if not, it ends with the ellipsis. Such examples include infinite decimals (rational or irrational), sequences, series, recursive functions, and sets.
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Old December 3rd, 2012, 03:36 AM   #66 (permalink)
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Originally Posted by jhawkkw View Post
.99999... does in fact equal 1 and can be easily mathematically proved.

Let x=.9999999......
Therefore 10x=9.99999.......
10x-x =9x. == 9.99999.....-.999999....=9
So 9x=9
9x÷9 = 9÷9
Therefore x=1 which was equal to .999999... originally.
don't let students know that (some profs say that 69.999 doesn't equal 70, lol)
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Old December 3rd, 2012, 09:01 AM   #67 (permalink)
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don't let students know that (some profs say that 69.999 doesn't equal 70, lol)
some of you just dont seem to get it what is being wrote.

69.999 does NOT = to 70.

69.999... = 70; where the "..." means that the "9" is repeating to infinity.

.999... = 1
.999 not = 1
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Old December 3rd, 2012, 11:42 AM   #68 (permalink)
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Originally Posted by palmtree5 View Post
Never thought I'd see calculus references here...
Hang around here long loung enough, and you will learn that all calucuus is wrong, too.

Quote:
Originally Posted by h4x0rj3ff View Post
It depends on the setting really. If your manufacturing gears with a wire edm then .9999 is still .0001 underside from 1.00000. now if you have a geometric tolerance of lets say +- .00001 than that dimention being at .9999 would bring you out of tolerance by .00009 rendering the part non conforming and scrap.
But if you are baking brownies, how much does a pinch equal? Tell me that, my machinst friend?

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Originally Posted by scary alien View Post







Don't forget that the ellipses ("...") at the end of ".999..." are very important / significant.



Not in the world of Internet math, not one darn bit. So I will choose to ignore them altogether!

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Originally Posted by wyndslash View Post
don't let students know that (some profs say that 69.999 doesn't equal 70, lol)
Dont need no stinking proof. Fact is, 69.99 does NOT equal 70. Not if you divide by zero.zero, then you get a whole different number.
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Old December 3rd, 2012, 01:10 PM   #69 (permalink)
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This thread is still alive?
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Old December 3rd, 2012, 01:14 PM   #70 (permalink)
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Yep.


So 0.999999... + 0.00000...1 = 1.00000.....1?
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Old December 3rd, 2012, 01:25 PM   #71 (permalink)
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The ... means the 000 continues infinitely, so you can't tack a 1 on at the end.

If you want to say 0.999999...+ 0.000000000000000000000000000000000000000001= 1.000000000000000000000000000000000000000001 then I would agree with you.
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Old December 3rd, 2012, 01:35 PM   #72 (permalink)
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Pie goes to infinity. Its not recurring. This .000 recurring with a 1 on the end. It has as much right to exist as any other infinite number so don't avoid the question
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Old December 3rd, 2012, 01:41 PM   #73 (permalink)
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That's different, pie is a known number. The question you phrased wasn't a known number nor was it an infinate number because you expressed it ended in 1

If you want to say

0.999...+0.(x)1

Where x is a set number of 0s, then yes that would be 1.(x)1.
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Old December 3rd, 2012, 01:57 PM   #74 (permalink)
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How is my number not known? You can get it from a simple subtraction.

1 - 0.9999....
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Old December 3rd, 2012, 02:03 PM   #75 (permalink)
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Its not a known number because you implied the 0s repeated for infinity and then ended in 1. An infinite number doesn't end.


But this whole conversation is about how .999...=1

1-0.999...=x
1-1=x
X=0
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Old December 3rd, 2012, 02:09 PM   #76 (permalink)
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Its not a known number because you implied the 0s repeated for infinity and then ended in 1. An infinite number doesn't end.


But this whole conversation is about how .999...=1

1-0.999...=x
1-1=x
X=0
No because you assume in this that 0.9999... = 1 which it doesn't. If 0.9999... = 1 and the problem is set out to either prove or disprove that, you cannot make the assumption within the problem. It must be the outcome.

Its like using the word you are defining in definition.


Even though Wikipedia says .9999... is 1, its not
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Old December 3rd, 2012, 02:18 PM   #77 (permalink)
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I'm saying you cant get the number you presented from the equation given

I digress, we wont keep running circles with the same points. Someone else can chime in.

Have a good one.
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Old December 3rd, 2012, 02:25 PM   #78 (permalink)
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SUroot,

the issue is.. you expressed an infinite reoccurring "0".. but tried to add and end to it with a "1".

the issue is.. how can it be? infinite means to go on FOREVER.. there should be no end. once you put and end to it.. then it is not infinite. see the problem?
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Old December 3rd, 2012, 02:36 PM   #79 (permalink)
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Yes dan330. I "get" the problem. You're saying I can't have an infinite number and round up by a 1 at "the point at infinity", even though we did that to get 0.999.... to become 1
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Old December 3rd, 2012, 03:12 PM   #80 (permalink)
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Ok I'm going to give up now. Mathematically it is unprovable that .999... does not equal 1, even though it doesn't, logic tells us that but for those whom subscribe to maths' truth, logic is a feutile argument. Even using hyperreals, Riemann spheres and limiting cases it can always be refuted. It's unprovable both ways because its an infinite loop of refuting arguments where nothing is agreed except that 0.999... = 1 is a mathematical fact.

So y'all stick with maths and i'll stick with logic
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Old December 3rd, 2012, 03:29 PM   #81 (permalink)
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Ok I'm going to give up now. Mathematically it is unprovable that .999... does not equal 1,
.999... is a geometric series. Geometric series with the properties that .999... has converge to a finite number, and that number is easily calculated. This is provable, and is taught in all second semester calculus classes. Your belief is as mathematically incorrect as believing that

1 + (1/2) + (1/4) + (1/8) + (1/16) +...

does not equal 2, or that

.1111111...

does not equal 1/9.
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Old December 3rd, 2012, 04:04 PM   #82 (permalink)
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So as much as you argued 0.999... = 1, you're now saying you can prove the opposite, unrefutably? Go for it. Or did you misread what you quoted? If you didn't misread and you are countering the fact that it is unprovable without refute, you quoted out of context and missed the important part out.
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Old December 3rd, 2012, 04:33 PM   #83 (permalink)
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I screwed up the quote. Sue me.
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Old December 3rd, 2012, 04:39 PM   #84 (permalink)
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What's the address of your lawyer?

But seriously, if you have a mathematical example that goes a long way towards disproving 0.999... = 1, even if it's not unrefutable, I'd be interested to see it.
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Old December 3rd, 2012, 09:01 PM   #85 (permalink)
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I just want 1 cookie
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Old July 23rd, 2013, 02:04 PM   #86 (permalink)
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are you keeping the .00001 of that cookie?? selfish!!!!!
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Old July 23rd, 2013, 02:06 PM   #87 (permalink)
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This thread is back from the grave?
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Old July 23rd, 2013, 03:06 PM   #88 (permalink)
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I would imagine if you're working in very specific conditions where a micrometer makes a difference, absolutley not. But for the rest of the world, yes.
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Old July 23rd, 2013, 09:21 PM   #89 (permalink)
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Old July 23rd, 2013, 10:33 PM   #90 (permalink)
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Old July 24th, 2013, 02:27 PM   #91 (permalink)
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if you ask a computer you will get the answer of no.

bool isValid = false;
if(1 == .999)
{
isValid = true;
}
else
{}

isValid would stay false through that statement. If you're saying .999 = 1 you would have to say that 999 = 1000. Really it depends on what you're dealing with, if you have 999 in your checking account and you write a check for 1000 you're going to have a problem.
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Old July 24th, 2013, 02:31 PM   #92 (permalink)
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if you ask a computer you will get the answer of no.

bool isValid = false;
if(1 == .999)
{
isValid = true;
}
else
{}

isValid would stay false through that statement. If you're saying .999 = 1 you would have to say that 999 = 1000. Really it depends on what you're dealing with, if you have 999 in your checking account and you write a check for 1000 you're going to have a problem.
A computer doesn't have a way to store an infinite number of terms, and any terminating number of 9's will never be equal to one. The idea is that if the number has an infinite amount of 9's, then it's exactly equal to one.
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Old July 24th, 2013, 02:39 PM   #93 (permalink)
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Its not so much that your maths is wrong as it is that maths is wrong in general.
This ^

If math ("maths" to you brits ) were perfect everything would be perfect including the human brain that invented math.

To me, math is a handy myth. Handy in helping us to build things and go places, etc. Myth in that we can't rely on a system that self-negates, such as Pi, etc.
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Old July 24th, 2013, 02:59 PM   #94 (permalink)
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It may not have any way of storing the infinite numbers, but the logic would still be the same.

To me .999... does not equal 1, because 0.999... is not 1.000... the only way it is, is when you round, which then you are just changing the number.

When I go shopping I do round everything to the nearest .50/.00 to make it easier to calculate my spending. Just because I say its that number, doesn't actually make it that number. The fact of the matter is it stays unchanged just as .999 does.

My opinion
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Old July 24th, 2013, 03:11 PM   #95 (permalink)
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It may not have any way of storing the infinite numbers, but the logic would still be the same.

To me .999... does not equal 1, because 0.999... is not 1.000... the only way it is, is when you round, which then you are just changing the number.

When I go shopping I do round everything to the nearest .50/.00 to make it easier to calculate my spending. Just because I say its that number, doesn't actually make it that number. The fact of the matter is it stays unchanged just as .999 does.

My opinion
i think you are not on the same page as the OP question.

you are right... {.999} is not equal to 1.0
but we are discussing {.999...} (the "9" is repeated to infinity)
the infinity part is what makes the difference ..
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Old July 24th, 2013, 05:23 PM   #96 (permalink)
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i think you are not on the same page as the OP question.

you are right... {.999} is not equal to 1.0
but we are discussing {.999...} (the "9" is repeated to infinity)
the infinity part is what makes the difference ..
Right, its going on forever, we say it equals 1 but in reality it doesn't. Think of pi, we say it equals 3.14 and that's basically it, but it does not equal 3.14, as the number goes on forever.
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Old July 24th, 2013, 05:28 PM   #97 (permalink)
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Right, its going on forever, we say it equals 1 but in reality it doesn't. Think of pi, we say it equals 3.14 and that's basically it, but it does not equal 3.14, as the number goes on forever.
3.14 is an approximation for pi, just like 22/7 is an approximation for it. 1 is not an approximation of .999..... repeated for ever because it can be proven that they are equal. There are several proofs, 4 to be exact, in earlier posts in this thread showing that.
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Old July 25th, 2013, 06:15 AM   #98 (permalink)
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3.14 is an approximation for pi, just like 22/7 is an approximation for it. 1 is not an approximation of .999..... repeated for ever because it can be proven that they are equal. There are several proofs, 4 to be exact, in earlier posts in this thread showing that.
Its kind of odd to think that .999 = does in fact = 1. for me at least.
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Old July 25th, 2013, 06:38 AM   #99 (permalink)
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Its kind of odd to think that .999 = does in fact = 1. for me at least.
Yeah, it's one of the oddities that show up in mathematics. There are other cases where two "different" looking things actually turn out to be the same. Graph/Group/Ring isomorphisms is an entire topic dedicated to where 2 different things that contain totally different elements can be proved to be the same because they a 1-1 mapping of their relationships.
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Old July 25th, 2013, 09:41 AM   #100 (permalink)
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Yeah, it's one of the oddities that show up in mathematics. There are other cases where two "different" looking things actually turn out to be the same. Graph/Group/Ring isomorphisms is an entire topic dedicated to where 2 different things that contain totally different elements can be proved to be the same because they a 1-1 mapping of their relationships.
I may be taking that sometime in college, I want to be a computer engineer, and that requires a lot of math, so... I have a lot of math classes to look forward to.
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