Poll: 0.999... = 1
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There's no theoretical end to infinity, either. Infinity is infinite, it has no end. At all. It might have a beginning, but never an end. It might be countable or uncountable, but it never, ever ends. Ever.Piflik said:
There is never a zero, there are only 9s. When you shift the digits left, it's still just 9s going on forever. If there's ever a shortage of digits, you could just shift it left and mine the integer part for a nine, then repeat (forever!).
Math is so simple, yet so easily misunderstood.
Jaime_Wolf said:
Och jaime. See, we (from my POV) don't even generally disagree with each other. I am very well aware, that i have been walking on very thin ice by making a distinction between numbers and processes (the connection is that "values" (i dont know the right word) can indeed be represented as direct numbers as well as processes, so that indeed a process and number can refer to the same value). We're on the same line about the background-theory.
What i disagree with - as hinted earlier - is purely the definition of the "term" infinity. See, i'm someone who defines a lot of things different than others. That is because i do not just accept terms simply because someone says so. I look at how the terms are used, how they are related to other terms, and so on - so, i have a tendency to define terms according to which meanings are actually communicated with them (instead of the claimed meaning). I'm aware that this approach has some pitfalls and issues, but while being aware about them, this approach has served me very well for many years.
In the case of infinity, i look at what happens in practice when it is used. And that is simply a repetition-process. That this is how most people understand this term, is all too visible precisely with the 0.999... question. When someone says "add 9's infinite times", then i take it to mean just that.
Sure, you can argue that how doing precisely this, makes little sense, if one considers the theoretical backgrounds - and that therefore, we should "correct" the result to what makes sense. I don't even disagree that "functions" like this should work different than "infinite times 9". But as mentioned earlier, if the instruction should be different, then use a different instruction, not the "wrong" one with the "right" meaning.
So, our disagreement ultimately is simply one of language, not one of concept.
It isn't equivalent to zero. That was my point, infinity is the concept of "as close as you can get without being it"... Kinda. 1x10^(-infinity) would equal 0.(an infinite number of zero's)1.smithy_2045 said:
Basically, the difference between 0.9 recurring and 1 is infinitesimally, immeasurably small. But they are not equal.
popa_qwerty said:and this world of empty space is nothing but what we conseve it to be;;psGlademaster said:I hate this theorem worse than the making 2=1 through dividing by 0.havass said:
OT: Yes technically speaking in maths 0.9999... is equal to one. For more counterintelligence ideas. Since every atom is mostly empty space me, you, your family, the walls around you and everything you have ever known is mostly empty space. Thus everything ever is a waste of space.
pardon my bad English[/quoteMeh
Meh it's fine. Only 1 word spelt wrong. Although it is funny how we never actually touch thigns either on an atomic level.
Yes, very good, but can you demonstrate why 0.999... is not equal to 1? Here, I'll prove that it is, and you can try and find a problem with my proof.Pirate Kitty said:
Redingold said:
Really? I suppose you have some strong, alien mathematics where 0.999... is not equal to 1, then. Could I see it?Rainforce said:
Yes, very good, but can you demonstrate why 0.999... is not equal to 1? Simply saying that they are each equal to themselves does not show that they are not equal to each other. Here, I'll prove that 0.999... is equal to 1, and you can try and find a problem with my proof.Pirate Kitty said:
Redingold said:
Really? I suppose you have some strong, alien mathematics where 0.999... is not equal to 1, then. Could I see it?Rainforce said:
Infinity is not "as close as you can get without being it", the term you're thinking of is asymptote - approached infinitely close, but never met. Infinity is anything it damn wants to be, it could approach, it could meet, it could intersect. There's no such thing as a 1 in the end of an infinite string of 0s. 10[sup]-infinity[/sup] equals 0. It is equivalent to zero. It's not asymptotically close to zero (as you propose), it is zero.brunothepig said:
I need some popcorn.
but the more u add the more the difference between the 2 becomes apparent no? i mean no 1 will consider 999,999.99 = 1,000,000.00 your always short. but i guess if you never expand .999+ sure its equal to 1. I believe the entire movie of Office Space depends on this lol
No...sorry, but you're wrong. You cannot shift the digits in any number and just call it a day. Infinite or not. If you take 0.9999... and multiply it with 10, there is a 0 at the end, not a 9. Regardless of how many 9s you write in that number. If you want to prove me wrong, you would have to actually write that number with infinite 9s, and even if you can pull that one of, I still assume that there would be a 0 at the end when you multiply it with 10...Coldie said:
Actually, there really is no such thing as infinity. It is a theoretical concept, but it doesn't exist. Every number has an end. Always.
That counterargument is so....... i dont even know why i pressed the reply button. The only thing 0.000... has in common with 0.999... is the instruction to repeat digits - except of here: THEY SERVE NO PURPOSE - THE TARGET WAS ALREADY REACHED BEFOREHAND.Coldie said:
Sorry you're right, that was a clumsy way of saying it. I'm tired...Coldie said:
Anyway, I remember talking about my math teacher with this, and he told me how to debunk it, but I've forgotten... Like so many other things from my Specialist Mathematics class... I'm just gonna have to say, they aren't equal, but I forget how to prove it. I believe it's a proof by contradiction... Google it if you want.
Enjoy your popcorn.
Wrong. Consider multiplying 0.999... by 10. The second decimal place becomes the first decimal place, the third decimal place becomes the second decimal place and so on. The n+1th decimal place becomes the nth decimal. However, the n+1th decimal place is a 9, because every decimal place is a 9. Thus, when we've multiplied out number by 10, every nth decimal place will be a 9.Piflik said:
Also, pi goes on forever.
Infinity is very prominent a mathematical concept. It's quite real, I assure you. And, as redundant as it is redundant, infinitely long numbers are, in fact, infinitely long. They never have an end. Here, let me show you, an infinitely long number that has an infinite number of digits after the decimal point and no end ever:Piflik said:
Quite a famous transcendent number, especially prominent in trigonometry and geometry. Also it's infinitely long and has a finite value.
Some infinitely long numbers have a repeating pattern, for instance 1/3 is just infinitely repeating threes. The notation for such numbers is 0.(periodic pattern), so 1/3 = 0.(3) or 1/7 = 0.(142857).
So if you take 0.(9): 1 - 0.(9) = 1 x 10[sup]-infinity[/sup] = 0.
You can find the detailed calculations in the first couple pages of the thread.
Don't try to understand it, just accept it as the universal and absolute truth. Because that's what it is. Elementary Arithmetics.