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o snaps.. so many replies haha thanks yall for putting in your insights... well today i took my solution to my professor in class.. and he said that this paradox cannot solved by mathematics, instead you have to take it from a philosophical perspective. This is what I said to him in class:
"As you break down the 100 meters into many intervals, up to an infinite amount, the distance of each interval then becomes smaller and smaller; which then means that the distance of each interval begins to approach zero, not infinity.. which means that each interval is a finite amount, thus it can be covered."
He then said to me that I make an excellent point, and he thought that a few years ago it would be the correct solution (not sure what that meant). However, he said that this problem is more about time than distance, the correct way to look at this is to look at the time it takes to cover each interval. Each interval is assigned a temporal value, and the total time is infinity, thats what matters. He then told me that math is not the way to solve this paradox, as advanced mathematics didn't exist in 500 BC, when this was first supposedly disproven. Well gotta think aabout it more then. Peace.
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it's the same as
lim (x->1) (x^2-2x+1)/(x-1)
you do the inside operation first, then apply the limit.
if you are taking infinity/infinity, then that is indeterminate, it's value doesnt exist
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can someone explain the achilles and the tortoise paraddox? Too lazy to google it~_~ if you can, also post how it is proven wrong.
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tortoise leaves point a time 0.
achilles leaves point a time 10.
although achilles moves faster than the tortoise, he will never catch him, because while achilles moves closer to the tortoise, it moves a little further forward.
http://mathworld.wolfram.com/ZenosParadoxes.html
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hydro what course are u taking?
Philosophy?
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I think you should have just handed in a blank piece of paper, and when he asks you what it was, just say you are unable to argue with zeno because motion does not exist, hence you couldnt write your essay.
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Hydrolisko, I told you how to approach it.
Let's assume the runner covers a 100m track in 10 seconds.
Let Zeno divide the distance infinitely (so he gets infinitely small distances) and you divide the time needed to run the distance (so you'll get infinitely small time). Whatever operation Zeno does with distance you apply that to time.
Now he tries to tell you that running that partial (infinitely small) distance takes a certain amount of time (which you keep a track of), and running all of them (which sums to 100 meters) will take infinity. Now you should ask him why the partial distances sum up to a nice finite number (100m) and the partial times (which were divided the exactly same way) would sum up to infinity? They should, in the very same way, sum up to 10 seconds. And that's all.
It just sounds stupid without using math though.
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On July 26 2005 18:41 Krzych wrote:
They should, in the very same way, sum up to 10 seconds. And that's all.
Isnt that the paradox? That they should, but they dont... I dont think youre understanding the argument or youre making assumptions which they dont make. Like saying that we can time how long it takes, hes saying we cant time it. Hes arguing for monoism, that everything is one and that there is no change. We arent moving 100m just as 10 seconds didnt take place, there is no change. Now argue it without all the assumptions you used that are what the argument is about.
If something weighs one gram, you split that into an infinite amount of parts each part weighs something (it cant just not exist anymore) and anything x infinity = infinity. So therefore 1g weight the same as the universe. In 10 seconds, you can break that down infinite times and each time will be a certani amount of time, that amount of time x infinity = infinity, thus 10 seconds and 68982389423940 billion years are the same amount of time ... infinite. You dont run 100m in 10 seconds, hes saying motion and time dont exist, there is no change.
Your post is just so full of assumptions that you assume we will infer. Its kind of written like that last sentence.
Just say that motion isnt infinitely constant or we are unable to understand infinite.
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No NO nONONONONON
Just argue that the sum of an infinite number of things IS NOT NECESSARILY INFINITE. PROVIDE AN EXAMPLE. HIS ARGUMENT DOES NOT HOLD. DONE
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On July 26 2005 19:09 BigBalls wrote:
No NO nONONONONON
Just argue that the sum of an infinite number of things IS NOT NECESSARILY INFINITE. PROVIDE AN EXAMPLE. HIS ARGUMENT DOES NOT HOLD. DONE
Then provide your example. Of course he is going to argue that the sum of infinite number of things isnt infinite otherwise we would be monoists.
He is using the old definition of infinity, the one that basically the whole world believes in still to this day. That infinity is endless. How can something that is endless have an end?
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Sum (n=1 to infinity) (1/2)^n = 1
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which happens to be the exact thing zeno is hypothesizing is infinite
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the proof i remember of it.....
Define S_n = 1/2 + 1/4 + 1/8 + ... + (1/2)^n. Thus, S_n is the sum of the first n terms.
2*S_n = 1 + 1/2 + 1/4 + ... + (1/2)^n-1.
S_n = 2*S_n-S_n = 1-(1/2)^n-1.
Let n approach infinity.
lim (n -> infinity) S_n = lim (n -> infinity) 1-(1/2)^n-1 = 1-0 = 1. Done.
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I thought they proved that theory wrong, and they now use...
Sum (n=1 to limit) (1/2)^n = 1
Does 1/3 = .33333.......infinite ?
Can mathematics provide a number for 1/3?
Im too high right now to begin thinking about it. Disregard this.
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On July 26 2005 19:20 Triton wrote:
I thought they proved that theory wrong, and they now use...
Sum (n=1 to limit) (1/2)^n = 1
Does 1/3 = .33333.......infinite ?
Can mathematics provide a number for 1/3?
Im too high right now to begin thinking about it. Disregard this.
1/3 is approximately equal to .3 repeating (infinitely) and is considered an inaccurate calculation. Math has a number for 1/3 already. That would be 1/3 
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HnR)hT
United States3468 Posts
No, .3 repeating is exactly the same thing as 1/3.
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Just a question (I dont pretend to be amazing at math, i havent been in school for a number of years so any knowledge has long since left me).
In 1000000000 years will we be using the same system of mathematics? I dont believe we will be, and I believe that our system that we are using now (using words like approximately) will no longer exist. The reason our system is wrong is the same reason we are unable to fully disprove Zeno.
And going with Hnr)HT -- if .33.... infinite = 1 then what is .9999... infinite / 3. Is there a difference between 1 and .999... infinite then? Im fairly certain that all this infinite isnt actually used anymore, and they use limits instead... So instead of disproving infinite (other than saying I am moving right now which I am perfectly okay with) we just conveniently choose to use something else instead.
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What? I just completely disproved Zeno. He made a false assumption in his argument, thus the conclusion he makes is worthless.
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On July 26 2005 19:41 BigBalls wrote:
What? I just completely disproved Zeno. He made a false assumption in his argument, thus the conclusion he makes is worthless.
Thomson's lamp
From Wikipedia, the free encyclopedia. ( http://en.wikipedia.org/wiki/Thomson's_lamp )
Thomson's lamp is a puzzle that is a variation on Zeno's paradoxes. It was devised by philosopher James F. Thomson, who also coined the term supertask.
Consider a lamp with a toggle switch. Flicking the switch once turns the lamp on. Another flick will turn the lamp off. Now suppose a being able to perform the following task: starting a timer, he turns the lamp on. At the end of one minute, he turns it off. At the end of another half minute, he turns it on again. At the end of another quarter of a minute, he turns it off. At the next eighth of a minute, he turns it on again, and he continues thus, flicking the switch each time after waiting exactly one-half the time he waited before flicking it previously. The sum of all these progressively smaller times is exactly two minutes.
Questions
* If after two minutes the switch is no longer toggled, will the switch (and lamp) be in the on-state or the off-state?
* Would it make any difference if the lamp had started out being on, instead of off?
Contrast with Zeno's Paradoxes
Two notable features of contrast between Thomson's Lamp and Zeno's Paradoxes is that in the case of the lamp the focus is on two discrete positions and there is a pause between them. Several proposed solutions to Zeno's Paradoxes fail if there is a pause before each movement in the series.
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It says proposed solutions, nothing has been "proven" or "disproven" least of all by you.
I dont believe that 1 = (1/2)^infinite now calculate it for me to prove it to me... go ahead, you have til infinity to finish.
edit: times up
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No offense, but i'm a 4th year math major who finished his math degree 2 years ago and im not going to argue with a stoner about something i already proved.
but thomson's lamp paradox is a nonsensical question. It's the equivalent of asking if the last integer is even or odd, which doesnt make any sense.
just for your own curiousity...
http://mathworld.wolfram.com/ZenosParadoxes.html
The resolution of the paradox awaited calculus and the proof that infinite geometric series such as can converge, so that the infinite number of "half-steps" needed is balanced by the increasingly short amount of time needed to traverse the distances.
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EPT
