I thought calculus was a robot in the cartoon "Futurama"? oh wait that was calculon...sorry This thread has gone clear over my noggin!

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.

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.

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. 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.

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

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.

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?

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.

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

Hang around here long loung enough, and you will learn that all calucuus is wrong, too. But if you are baking brownies, how much does a pinch equal? Tell me that, my machinst friend? Not in the world of Internet math, not one darn bit. So I will choose to ignore them altogether! 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.

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.

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

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.

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