Poll: 0.999... = 1
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I didn't say that all of math was intuitive, I said that all of mathematics finds its base in intuition. Axioms, by definition, exist either to codify intuitions (intuitions that we find basic and inescapable) or to solve paradoxes that arise when those intuitions collide. The sort of austerity you describe is an illusion created by the latter type of axiom: the sort that are required to maintain consistency within the system described. The problem is that when we take our basic intuitions and attempt to form more complex naive theories by extrapolating from them without extreme care, we introduce errors into our computation. Mathematics is, in essence, a way to perform careful extrapolation from our basic intuitions. It's ludicrous to claim any alternative. If mathematics doesn't stem from intuitions, where does it come from? You end up some sort of bizarre Platonist. Intuitions are all you've got. If you're actually interested in these questions, you should look into the philosophical foundations of mathematics and philosophy of science in general. There's some good discussion in the developmental psychology literature regarding acquisition of number theory as well.Coldie said:
People who know mathematics do not necessarily know the underpinnings of mathematics and it's statements like this, talking about how mathematics is somehow disjoint from reality and intuition, that lead the general public to reject complex mathematical results.
RE the actual question: If you don't think .999...=1, you probably think that it's less than 1. If it's less than one, you need to add something to it to make it one. What are you going to add? .000... with a 1 and the end? If there are an infinity of zeroes, WHAT END?
The issue of infinity as a number not being useful in the real world is also blatantly false. Many of these issues are extraordinarily important in physics and engineering. See therodynamics, hydrodynamics, and electrical engineering in particular (specifically regarding complex analysis).
This is a question of limits for asymtotes, and the function used to obtain these values is called lim.
So for this case is
lim(x)=1 for x -> 1
It's used in the proof of integrations and differentials. Where you slice the lines infinately thin and then add up.
So for this case is
lim(x)=1 for x -> 1
It's used in the proof of integrations and differentials. Where you slice the lines infinately thin and then add up.
I think anything that tries to grasp at infinity is flawed. Even if just on the grounds that one can't possibly understand what it doesn't know.
No one knows what happens once you count to infinity. Because as living creatures we cannot. I assume the clouds open up, God rides a flaming unicorn to the front of your house/apartment, and proceeds to teach you how to actually beat The Sims.
PS: No your Sims dying without children doesn't constitute *beating* the game. Duh.
No one knows what happens once you count to infinity. Because as living creatures we cannot. I assume the clouds open up, God rides a flaming unicorn to the front of your house/apartment, and proceeds to teach you how to actually beat The Sims.
PS: No your Sims dying without children doesn't constitute *beating* the game. Duh.
I really don't want to read all post and people might have said this, butRawle Lucas said:
9.999... = 9 + x =/= 10x - x = 9x = 8.99999999...
But if you don't want to be exact, you can always say that 0.99999 is 1. But there is no equal sign in there. Two different numbers are not equal.
And this is why we have different number sets like rational, irrational and real numbersepninja said:
Maybe I'm not being scientific enough but, isn't the answer that it's close enough that no-one should really care if it is or not?
If I had to choose between a million bucks and 0.99999... of a million bucks, I wouldn't waste a lot of time thinking about it. (it'd be the million because the other option might be a trap.)
If I had to choose between a million bucks and 0.99999... of a million bucks, I wouldn't waste a lot of time thinking about it. (it'd be the million because the other option might be a trap.)
Doesn't matter how much algebra you do, 0.999999999 of anything is less than a complete one. Therefore, they are not the same.
Why is everyone seeming to argue that this infinity needs to be calculated in real time?Klopy said:Some of the math in this thread is flawed... jeez. Double check, please.
.9999... is not equal to 1.
Why?
Still being in high school, and with my chemistry background, I would have to say that .9 etc. is not equal to 1 because of its significant figures. You can round up when the math is over, but it will never be correct. .9999999 will always be <1, no matter how close it gets. In the math world, this is just how it has to be.
In real life, it would get so close to 1 that it wouldn't really matter.
But in theoretical conversations, it will always be <1.
By which I mean, people are saying "Sure, you can keep adding those 9s, but you'll never actually reach forever."
It doesn't reach forever, true. It just is.
It is infinite, right now. It won't "never reach forever", it is forever already.
That's what infinite means.
I...I don't get what's difficult about that.
Still, not a Math Major here, maybe infinity is treated differently in maths. I'd find it difficult to calculate with an infinity that actually equalled an ever-fluctuating rational number though, myself.
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.
