16 May 05
Originally posted by davegageInteresting. Only now I've noticed you said in finite time in the other post.
I agree that all the series you are refering to diverge -- that is clear since the assumption we are working with is that the farmers' rows are infinite. But I don't think this answers the question, which deals primarily with cardinality.
Consider again the case where the farmers plant the first seed in 1 second, the second seed in 1/2 of a second, th ...[text shortened]... y said you agree with Premise 1. So if you reject Premise 3, then what is wrong with Premise 2?
My maths are a bit rusty and I have to go, but I'll come back later to try and find out what the sum of the crows series would be after 2 seconds. If that makes sense.
I'm beginning to agree with you.
16 May 05
A related issue I find interesting the matter of the number .9repeated. It is accepted that this "number" equals one: .9 repeated*10=9.9repeated and 9.9repeated - .9repeated equals 9, so 9(.9repeated)=9 and .9repeated=1. However these are not logical conclusions.
It doesn't make sense to say there is 1 less than infinity 9's. If it is then what is infinity-1=? Well I will also ask what is x-1=? You can't get an answer for either of them because neither of those "numbers" can be defined. And who can grasp infinity?
16 May 05
Originally posted by bobbob1056th*raises hand*
A related issue I find interesting the matter of the number .9repeated. It is accepted that this "number" equals one: .9 repeated*10=9.9repeated and 9.9repeated - .9repeated equals 9, so 9(.9repeated)=9 and .9repeated=1. However these are not logical conclusions.
It doesn't make sense to say there is 1 less than infinity 9's. If it is then what ...[text shortened]... either of them because neither of those "numbers" can be defined. And who can grasp infinity?
I can grasp infinity!
16 May 05
Originally posted by bobbob1056thUgh again.
A related issue I find interesting the matter of the number .9repeated. It is accepted that this "number" equals one: .9 repeated*10=9.9repeated and 9.9repeated - .9repeated equals 9, so 9(.9repeated)=9 and .9repeated=1. However these are not logical conclusions.
It doesn't make sense to say there is 1 less than infinity 9's. If it is then what ...[text shortened]... either of them because neither of those "numbers" can be defined. And who can grasp infinity?
No, this is most definitely not the way you prove 0.99999..... = 1.
You can show this equation holds (with no ambiguity) if you appeal to some much more formal mathematics in the field of real analysis, for example. No, I don't want to get into that, but suffice it to say you are confused because you are confusing yourself.
You also seem to be under the impression that just because you cannot grasp infinity, then no one else can either. This is not a logical conclusion for you to draw.
16 May 05
Originally posted by davegageNo, you cannot prove something that is false, and it is impossible to grasp infinity, else there would be definite answers to questions like what is infinity minus infinity=?
Ugh again.
No, this is most definitely [b]not the way you prove 0.99999..... = 1.
You can show this equation holds (with no ambiguity) if you appeal to some much more formal mathematics in the field of real analysis, for example. No, I don't want to get into that, but suffice it to say you are confused because you are confusing yourself.
You ...[text shortened]... grasp infinity, then no one else can either. This is not a logical conclusion for you to draw.[/b]
17 May 05
Originally posted by bobbob1056thIf 0.99999.... = 1 is false, then prove it. (This is an exercise in futility since it is true.)
No, you cannot prove something that is false, and it is impossible to grasp infinity, else there would be definite answers to questions like what is infinity minus infinity=?
The reason why you are baffled by questions like 'what is infinity minus infinity' is because you clearly don't understand the concept of cardinality. Go educate yourself about these things.
Normally I wouldn't target someone's posts like this, but the way you put forth utter hogwash as though it were provable fact is just too arrogant to ignore.
I also find it humorous how you argue matter-of-factly about infinity while simultaneously admitting that nobody (and thus also you) cannot understand it.
17 May 05
Originally posted by bobbob1056thSomething is considered true if it is proven true, not if it hasn't been proven false.
Something is considered true if it is proven true, not if it hasn't been proven false. Why don't you show why you think .999... = 1? even if I am wrong I'd like to see a valid explanation as to why this holds true.
I agree.
Why don't you show why you think .999... = 1? even if I am wrong I'd like to see a valid explanation as to why this holds true.
Certainly. I haven't the time at the moment, but I will formulate an argument, make it as coherent as I think possible, and then I will post it later tonight. Hopefully it will be convincing.
17 May 05
Originally posted by PalynkaYes it is, because whatever number seed you pick, I can give you a unit of time when it got eaten. If every seed gets eaten, there are none left. Every seed gets eaten when the alloted time has ellapsed, so there are no seeds left.
I agree, but:
Quoting from the original post
[b]there will be no seeds left in his row, for bird B will eat every one eventually.
The second conclusion is correct, but the first one is not.[/b]
A twist to this problem is a light bulb problem. Anticipating the jokers that will say the bulb will burn out, this bulb does not burn out. Suppose you have a bulb that you switch on at two minutes till midnight, and leave it on for a minute. Then at a minute to midnight you turn it off, and leave it off for 30 seconds. At 15 seconds to midnight you turn it back on, and you get the gist. Anyway, is the bulb on, or off at midnight? The answer is... It is neither on, nor off, which is hard to comprehend for a binary function.
17 May 05
1/3 = .3 repeating
.3*3 = .9 repeating
1 = .9 repeating
not a perfect proof by any means, but you should get the idea.
now,
can a "random" occurrence truly exist?
can a humidifier fight a dehumidifier to the death?
and
how many times do you have to pour vodka through a water filter before it starts to taste sweet?
17 May 05
Originally posted by bobbob1056thFirst, I would say that this topic has already been extensively debated in this forum (check the archives) and elsewhere on the internet, but I don't really see what there is to debate about it.
Why don't you show why you think .999... = 1? even if I am wrong I'd like to see a valid explanation as to why this holds true.
There are more formal ways to go about a proof of this equation, but I don't see the need to dust off my real analysis texts.
The following are different ways to see that this equations holds:
1. 0.9999.... = 9/10 + 9/100 + 9/1000 + .... (this should be obvious). Thus more generally, 0.9999.... = Summation(n = 1 to n = inf.)[9/10^n] = Limit(m -> inf.) of Summation(n = 1 to n = m)[9/10^n]. But Summation(n = 1 to n = m)[9/10^n] = 1 - 1/10^m. So 0.9999.... = Limit(m -> inf.) of [1 - 1/10^m] = 1 - 0 = 1.
2. 'Proof' by contradiction: I think you'll agree that 0.9999.... > 1 is clearly false. So we have that 0.9999.... <_or_= 1 must hold. Then suppose that 0.9999.... < 1 holds. Then there exists some nonzero positive number DELTA such that 1 - 0.9999.... > DELTA. You see where I am going with this...it's obvious that no such DELTA exists...all you have to do is carry the 9's out far enough, and you can always get (1 - 0.9999....) to be less than any such DELTA. Thus you reach a contradiction, thus 0.9999.... < 1 does not hold; thus we are left with only 0.9999.... = 1. That proof can be much more formal, but it's a real pain to try to type math in these posts.
3. Touchy-Feely proof: Consider that you are standing on the number line exactly at 1 and you are looking toward 0. Ask yourself how far you can walk toward zero before you overstep 0.9999.... Of course, you can go nowhere -- not even the tiniest little step. If you consider how large the separation is between 1 and 0.9999.... on the number line, I think it is clear that there is no such separation -- thus they are the same points.
I could continue to jump through hoops here for you, but I am interested to know how you would refute these claims, especially since your retort that something is considered true when it is proven true, not when it is not proven false is a clear cop-out -- I was proposing that '0.9999.... = 1' is true, and you were proposing that '0.9999.... = 1 is false' is true -- the burden falls on both of us.
17 May 05
Originally posted by slippytoadCould you translate this, please. I am not sure what you are refering to.
now,
can a "random" occurrence truly exist?
can a humidifier fight a dehumidifier to the death?
and
how many times do you have to pour vodka through a water filter before it starts to taste sweet?
17 May 05
Originally posted by slippytoad1. I think it depends on what you mean by "random". The definition I'm familiar with is this: a random event is one that cannot be predicted with absolute certainty. If you could predict it, it would be determined.
now,
can a "random" occurrence truly exist?
can a humidifier fight a dehumidifier to the death?
and
how many times do you have to pour vodka through a water filter before it starts to taste sweet?
2. I don't know - but I for one would like to setup a foundation to discover the answer. We could make money off the fight videos, like "Bumfights" but more tasteful. Who's with me?!?
3. I don't know. I just drink it. If I want it sweeter, I put orange juice in it.
17 May 05
Originally posted by davegageIs 0.9 = 1? no. is 0.99 = 1? no. How about 0.999? None of these numbers equal one, although the more nines you add the closer you get to 1. Your first conjecture doesn't prove anything, it just assumes that 1 - 0.999... = 0. Your second one: it doesn't make any more sense to have a number with an infinite number of nines after the decimal than it does to have an infinitesimally small number (namely, 0.000...1), so if you say the number 0.000...1 isn't unique (I presume you would say this number equals 0?) you'd have to prove it in the same way you'd have to prove 0.999... = 1. It's like saying (*any*) statement is true because (*any other statement that also hasn't been proven true*) proves it true and vice versa. That leaves you on square one. And for your third conjecture, as I said before, you'd get closer and closer but never reach 1, although this cannot be expressed using space because it would obviously be too difficult to show extremely small distances.
First, I would say that this topic has already been extensively debated in this forum (check the archives) and elsewhere on the internet, but I don't really see what there is to debate about it.
There are more formal ways to go about a proof of this equation, but I don't see the need to dust off my real analysis texts.
The following are different w ...[text shortened]... you were proposing that '0.9999.... = 1 is false' is true -- the burden falls on both of us.
Also, is it accepted as a fact that sum(1/2, 1/4, 1/8...) does not equal 2?