Some of the random uninformed "rebuttals" are pretty hilarious. You can almost hear their little brains explodering.
It's easy to get the same response with the race car riddle, too; I've had folks get all but violent denying the math.
quote:
A race car driver trying out a new car on a 1-mile track wants to drive two laps with an average speed of 60mph to verify the on-board computer. If he averages 30mph on the first lap, how fast will he have to go on the second to achieve his goal?
--Satan, quoted by John Milton
quote:The speed of light.
A race car driver trying out a new car on a 1-mile track wants to drive two laps with an average speed of 60mph to verify the on-board computer. If he averages 30mph on the first lap, how fast will he have to go on the second to achieve his goal?
quote:
Quoth `Doc:
The speed of light.
Doesn't work for the observer with the stop watch and calculator, sorry. 
--Satan, quoted by John Milton
quote:
Bent over the coffee table, Katrinity squealed:
While its the obvious answer (in my mind anywho) and probably not the right one, I'm gonna go with 90mph.
You're correct! [small]That's the obvious, but not the right, answer.[small]
--Satan, quoted by John Milton
you! 
. Infinte math comes in handy when thinking about concepts such as the volume and/or shape of the universe, time travel and similar phenomena, the unreachability of absolute zero temperature, or the realm of possiblities.
.9~ converges to 1, but they are different and can't be substituted for one another in all cases.
quote:
Quoth `Doc:
With regards to the subject of the article itself, I tend to think of .9999... as one minus infinitesimal zero, to be treated as one minus zero, also known as one, in finite mathematics (which ignores infinitesimal values). The only real difference is that, if you plan to work in and/or through infinite and/or infinitesimal values, then (1/0)/(1/0) could still come out to 1, as could (0/1)/(0/1). Either operation, when attempted in finite mathematics, has a result of
you!
.
Infinte math comes in handy when thinking about concepts such as the volume and/or shape of the universe, time travel and similar phenomena, the unreachability of absolute zero temperature, or the realm of possiblities.
You're free to think of it like that, of course, but the fact remains that there is zero mathematical difference between the two.
--Satan, quoted by John Milton
After driving for two minutes, he still has one mile left. His time is up.
The obvious answer is that he has to drive bribery miles an hour.
edit: Just in case it's a trick question. It depends on how the computer works. Technicly, he will be at his goal from a GPS perspective. So it really depends on how the software works and if he can "trick" it. diadem fucked around with this message on 12-05-2006 at 05:51 PM.
diadem fucked around with this message on 12-05-2006 at 06:00 PM.
Sometimes, I imagine that it must be similar for people who have a hard time with complex sentences.
However, just as everyone knows basic math, I cannot excuse someone not knowing basic English.
quote:
Verily, the chocolate bunny rabbits doth run and play while diadem gently hums:
won't let me edit my edit... In reality, the ultimate goal would be to check the accuracy of the trip computer, not to complete the lap in a certain amount of time. The lap is just a means to an ends. He completed a full mile with some clean numbers, so it might not be a total loss.
You've been distracted by the window dressing. His goal is to average 60mph over 2 laps.
--Satan, quoted by John Milton
code:8 * 10^0 + 9 * 10^-1 + 9 * 10^-2 + ... 9 * 10^(-(Infinity - 1)) + 1 * 10 ^(-Infinity)
The above divided by 9 simply reverts back to 0.9~ again. This is, of course, all really ugly theoretical math, with so much use of infinite numbers, and in the end doesn't really prove that 0.9~ != 1, only that the proof given is very sloppily done, with a mistake that's usually ground into children not to make in middle school.
Please forgive my ugly ascii math. >< Darkness fucked around with this message on 12-05-2006 at 06:30 PM.
quote:
Verily, the chocolate bunny rabbits doth run and play while Noxhil2 gently hums:
Isn't this really relativistic physics rather than math?
I fail to see the relevance of relativistic physics, given the situation and the fact we're talking about a car. And, as pointed out earlier, even if we posit infinite instantaneous acceleration to c, it doesn't solve the problem of an observer.
--Satan, quoted by John Milton
quote:
Verily, the chocolate bunny rabbits doth run and play while Darkness gently hums:
You know, there's a very simple flaw with his example of why 0.9~ = 1, and it's the bane of scientific mathematics everywhere: Significant Digits. 0.9~ would have an infinite number of significant digits to the right of the decimal point. 9.9~ would also have an equally infinite number of significant digits to the right of the decimal point, but also one significant digit to the left of the decimal point, thus demonstrably greater than the origin. Since he is multiplying, and the significant digits must remain the same, technically the end of the string representing 9.9~ in his equation must be at 9 * 10^(-(Infinity - 1)), so when you subtract 0.9~ fom his 9.9~, you end up with a string of:code:8 * 10^0 + 9 * 10^-1 + 9 * 10^-2 + ... 9 * 10^(-(Infinity - 1)) + 1 * 10 ^(-Infinity)The above divided by 9 simply reverts back to 0.9~ again. This is, of course, all really ugly theoretical math, with so much use of infinite numbers, and in the end doesn't really prove that 0.9~ != 1, only that the proof given is very sloppily done, with a mistake that's usually ground into children not to make in middle school.
Please forgive my ugly ascii math. ><
You fail, too. The conversion to fractions proof sinks your attempt. 1/3 = .33~ and if you multiply both by 3 you end up with 1 = .99~. That's by far the easiest and most intuitive proof for the concept.
--Satan, quoted by John Milton
quote:
And then there are the
SPIRITUAL implications.9 a soul
+ .09
+ .009 adding experience
+ .0009
+ .00009
!
! infinitely increasing
!or the infinitely
repeating process
of growing greater
i.e. life--------
.99999---which EQUALS
1
the finished, static, unity
characteristic of a single
never-created beingi.e. God
The equations show
IT MADE US TO BE ITS EQUAL
(the TRUTH behind all men
are created equal -
soul A = God,
soul B = God
transitive property -
A = God = B therefore A=B)but .999--- being = 1
and 1 being a rational
number, 1/1 is the ratio
of two integers, as a guy
named Hugh Richmond asked
me, where are the two
integers whose ratio is
.999---
THERE ARE NONE thus
I coined an equation to
go with .999--- = 1 which
demonstrates our equalityx/y = .999---
where x and y are integersTHAT equation show the
DIFFERENCE between the
Creator and the Created -
only the Creator can make
it work.
Disclaimer: I'm just kidding, I love all living things.
The fastest draw in the Crest.
"The Internet is MY critical thinking course." -Maradon
"Gambling for the husband, an abortion for the wife and fireworks for the kids they chose to keep? Fuck you, Disneyland. The Pine Ridge Indian Reservation is the happiest place on Earth." -JooJooFlop
quote:
From the book of Bloodsage, chapter 3, verse 16:
You're correct! That's the obvious, but not the right, answer.
What's the right answer then? This is making my brain hurt.
quote:
What's the right answer then? This is making my brain hurt.
His goal essentially being to drive 2 miles in 2 minutes, and already having taken 2 minutes to complete the first lap, he would have to complete the final lap without any time elapsing, thus dividing by zero and forcing God or Stephen Hawking to come fix the resulting apocalypse. Darkness fucked around with this message on 12-05-2006 at 07:19 PM.
quote:
How.... Darkness.... uughhhhhh:
His goal essentially being to drive 2 miles in 2 minutes, and already having taken 2 minutes to complete the first lap, he would have to complete the final lap without any time elapsing, thus dividing by zero and forcing God or Stephen Hawking to come fix the resulting apocalypse.
So it's kinda like a question in a question. Or something.
quote:
Bloodsage had this to say about Captain Planet:
You've been distracted by the window dressing. His goal is to average 60mph over 2 laps.
Ok, so it WASN'T a trick question then. Figured my original post was what you were looking for. If you look at the way it's phrased it could also be a trick to see if you get too caught up in the means to realize what the goal is (it stated that the reason he is doing the laps was to calibrate his computer). Pretty much the difference between getting asked a question in academia (to prove you understand concepts to reach the stated goal.. the situation as a whole being irrelevant and just dressing) and the business world (what's our end goal - WHY are we doing what we are doing? how do we get there? this is what we have to work with).
You asked a simple question and wanted a simple academic answer. Speed is distance over time and he has no time left. Hes up the proverbial creek.
edit: Aleph-naught miles per hour is NOT a speed, as far as I am aware (or alph-whatever.....) diadem fucked around with this message on 12-05-2006 at 08:53 PM.
quote:
So it's kinda like a question in a question. Or something.
*Nod* It can also be considered a question without an answer, like a tree falling in the woods, or whether 1/11 ends on a 0 or a 9. The whole "is 0.9~ = 1?" question is fairly similar. If I asked you to prove that 1 != 2 verbally, you'd likely be at a loss to do so, beyond telling me that, by the accepted definition of 1 and 2, they aren't equal. The accepted definition only exists, however, because it can be proven through physically observable means. Imaginary mathematics, using numbers like 0.9~ or Infinity, can't be physically proven, so we can only rely on the verbal definition we've given them to describe what they actually are. If, say, I define 0.9~ as != 1, and Bloodsage defines 0.9~ as = 1, neither one of us can ever truly prove our definitions, since every proof uses that same definition within itself. My proof is true, because my definition is true, because my proof is true, because... Discussions on infinity just provide infinite loops. 
... I kinda rambled there, WoW patch days drive me nuts.
quote:
Darkness wrote, obviously thinking too hard:
*Nod* It can also be considered a question without an answer, like a tree falling in the woods, or whether 1/11 ends on a 0 or a 9. The whole "is 0.9~ = 1?" question is fairly similar. If I asked you to prove that 1 != 2 verbally, you'd likely be at a loss to do so, beyond telling me that, by the accepted definition of 1 and 2, they aren't equal. The accepted definition only exists, however, because it can be proven through physically observable means. Imaginary mathematics, using numbers like 0.9~ or Infinity, can't be physically proven, so we can only rely on the verbal definition we've given them to describe what they actually are. If, say, I define 0.9~ as != 1, and Bloodsage defines 0.9~ as = 1, neither one of us can ever truly prove our definitions, since every proof uses that same definition within itself. My proof is true, because my definition is true, because my proof is true, because... Discussions on infinity just provide infinite loops.
... I kinda rambled there, WoW patch days drive me nuts.
In this context, the answer is that he can't do it. Once you realise this, you can explain it verbally.
edit: And you can do it without the recusrive problem you were talking about as well. Examples: Proof by contradiction (assuming your statement is false and proving that statement wrong), brute force (looking at every possibility), and simply looking at the facts stated and seeing how they reach a conclusion diadem fucked around with this message on 12-05-2006 at 09:44 PM.
Edit:
quote:
In this context, the answer is that he can't do it.
Ok, disprove the answer that he can, indeed, do it if he drives 1 mile in 0 hours, or 1/0 miles per hour. The fact that this is an unreal number, and he cannot physically move that quickly is irrelevant, since it is a direct theoretical answer to a direct theoretical question ("How fast would he have to go?", not "Can he go fast enough?"), as, if it were physically possible to go that speed, then doing so would satisfy the question. Darkness fucked around with this message on 12-05-2006 at 09:56 PM.
The formula for the average over two laps would be:
(x+y)/2 = 60
He averaged 30mph for the first lap, so
(30+y)/2 = 60
multiplay both sides by 2
30+y = 120
subtract 30 from both sides
y = 90
So if he drove 30mph for the first lap and 90mph for the second, his average for the two laps would be 60mph.
What's wrong with this?
Tegadil fucked around with this message on 12-05-2006 at 10:13 PM.
quote:
The logic train ran off the tracks when Maradon! said:
wait wait, I'm terrible at math but what's wrong with this:The formula for the average over two laps would be:
(x+y)/2 = 60
He averaged 30mph for the first lap, so
(30+y)/2 = 60
multiplay both sides by 2
30+y = 120
subtract 30 from both sides
y = 90
So if he drove 30mph for the first lap and 90mph for the second, his average for the two laps would be 60mph.
What's wrong with this?
So he traveled for two minutes and fourty seconds (two minutes for the first lap, fourty seconds for the second) and covered a distance of two miles. That means every mile he traveled takes one minute, twenty seconds. That, my friend, is not sixty miles an hour.
quote:
I was going to post a rebuttal with complete proof from 2(two) ASU mathematicians (who both agree with me), but upon review of all your posts, I came to the ultimate conclusion that you don't need proof. You will go to your grave believing with the core of your being that .9999999... does, in your mind, equal 1. However wrong I, or anyone else may think you are will not matter. Trying to convince you otherwise is like trying to convince an atheist that God exists.I leave you now, respectful of your opinion, because whether I agree or not is a moot point. You may choose to use personal attacks, call me a fraud, a liar, and an idiot, but I leave taking the high road. I bid you farewell, good sir.
"I was GOING to post incontrovertible proof that you're wrong but then I realized you wouldn't believe me, so I'm just going to leave. PS. I'm right and you're wrong."
WHERE HAVE I SEEN ARGUMENTS LIKE THIS BEFORE!? Maradon! fucked around with this message on 12-05-2006 at 10:29 PM.
quote:
Verily, Darkness doth proclaim:
Since I've already made more posts in this thread than I've probably made in all the rest of my time as a lurker, I'll add a bit to my earlier rebuttal to the 1/3 = 0.3~ proof that I'd forgotten. Once again, there is a significant digits error in that equation. 1.0~ has 1 significant digit to the left of the decimal point and an infinite number to the right of the decimal point, the same being true for 3.0~. 0.3~, however, only contains an infinite number of significant digits to the right of the decimal point, lacking the significant digit to the left of the decimal. Any time you lose a significant digit in your answer, you open yourself up to a round-off error, which in this case is that beyond-infinitesimal remainder I brought up earlier.Edit:
Ok, disprove the answer that he can, indeed, do it if he drives 1 mile in 0 hours, or 1/0 miles per hour. The fact that this is an unreal number, and he cannot physically move that quickly is irrelevant, since it is a direct theoretical answer to a direct theoretical question ("How fast would he have to go?", not "Can he go fast enough?"), as, if it were physically possible to go that speed, then doing so would satisfy the question.
Ok, fine. I'll throw the distance over time argument out the window.
He's traveling an infinate amount of miles per hour. Congradulations, you just passed your destination by - a lot.
Edit: Why is this an infinite amount of miles per hour?
Well, you said hes traveling at the rate of one mile every zero seconds. No time went by, so he moved another mile. No time went by again, so he moved another mile. No time went by again, so he moved another mile. You get the point - theres no end to it.
If he went the speed you explained over a period of zero seconds, he'd travel an infinate distance. That means he'd travel an infinate distance over the time span two minutes, which is much faster than 60mph. diadem fucked around with this message on 12-05-2006 at 11:11 PM.
TOO BAD, SO SAD.
quote:
Darkness was naked while typing this:
His goal essentially being to drive 2 miles in 2 minutes, and already having taken 2 minutes to complete the first lap, he would have to complete the final lap without any time elapsing, thus dividing by zero and forcing God or Stephen Hawking to come fix the resulting apocalypse.
...Were do you get the 2 Minutes from? Mayeb it is the late nigh hooch, but i see no time limit on the laps in the question.
From the strait mathamatics point of view he has to avarage 90mph like kat said I think. I can't think of putting more thought into it, doesn't seem like you need to.
If I travel 1 mile in 0 hours, i would be traveling 1/0 miles per hour.
If I travel 1/0 miles per hour, I will travel an infinate distance In the period of 0 hours.
If I traveled an infinate distance in the period of 0 hours, I did not travel exactly 1 mile in 0 hours.
Therefore, if I travel 1 mile in 0 hours, I can't travel 1 mile in 0 hours.
quote:
Peter had this to say about Tron:
...Were do you get the 2 Minutes from? Mayeb it is the late nigh hooch, but i see no time limit on the laps in the question.From the strait mathamatics point of view he has to avarage 90mph like kat said I think. I can't think of putting more thought into it, doesn't seem like you need to.
Sixty miles an hour is a mile a minute.
That means if you go two miles at sixty miles an hour, it will take you two minutes.
If you want to average sixty miles an hour over two miles, you will have to drive it in two minutes.
quote:
Peter was listening to Cher while typing:
...Were do you get the 2 Minutes from? Mayeb it is the late nigh hooch, but i see no time limit on the laps in the question.From the strait mathamatics point of view he has to avarage 90mph like kat said I think. I can't think of putting more thought into it, doesn't seem like you need to.
Because he drove the first lap at 30mph.
Go 60mph and you travel 1 mile in a minute. Go 30mph and it takes the entire 2 minutes for the first lap.
Edit: beaten =/ Reynar fucked around with this message on 12-05-2006 at 11:33 PM.
quote:
Ok, fine. I'll throw the distance over time argument out the window.He's traveling an infinate amount of miles per hour. Congradulations, you just passed your destination by - a lot.
Edit: Why is this an infinite amount of miles per hour?
Well, you said hes traveling at the rate of one mile every zero seconds. No time went by, so he moved another mile. No time went by again, so he moved another mile. No time went by again, so he moved another mile. You get the point - theres no end to it.If he went the speed you explained over a period of zero seconds, he'd travel an infinate distance. That means he'd travel an infinate distance over the time span two minutes, which is much faster than 60mph.
Actually, there's a small difference between an infinite speed and an instantaneous speed. (I'm going to use oo as shorthand for infinite, to save space) If you're going oo miles per hour, then you're still moving through time, since you're going oo miles in 1 hour. That means you'd move 1 mile in 1/oo hours, meaning the smallest non-zero amount of time possible, which still doesn't satisfy the question (He'd have moved 2 miles in just slightly over 2 minutes, instead of exactly 2 minutes.) To properly satisfy the equation, he has to cover exactly 1 mile with no time elapsing at all. At the point of "slightly more than 2 minutes," any actual speed and/or acceleration becomes completely irrelevant, since the original qualifications have been satisfied. It all comes down to the difference between imaginary, but possible, numbers, like infinity, and unreal, impossible numbers, like 1/0.
Edit:
Let's pose a new question: If Bob has 2 apples, and Jane has 3 apples, and Jane takes 3 apples away from Bob, how many apples does Bob have?
The circumstances of the question itself are impossible, but a theoretic mathematic answer still exists, the imaginary number -1. Darkness fucked around with this message on 12-05-2006 at 11:48 PM.
quote:
diadem was listening to Cher while typing:
Sixty miles an hour is a mile a minute.That means if you go two miles at sixty miles an hour, it will take you two minutes.
If you want to average sixty miles an hour over two miles, you will have to drive it in two minutes.
Again i fail to be seeing a time limit? He has to average 60 MPH over the 2 laps, he avarage 30 for the first, now he has to average 90 for the second lap. I don't see any limit in the problem to time, infact i read it as not giving a rats ass about how long it takes, just how fast his supper r-type gto ricer racer has to go. so i don't see how he has to go faster than the spped of light or something to make the secnod lap, he just need to average 90mph.
