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Abstract wrote:tralix the answer to you problem is
so is know one going to chance another guess at my problem?
Abstract wrote:no the next number is 7 now whats the next?
Abstract wrote:here is the answer then
Tralix wrote:Solve Zeno's paradox about firing an arrow and never being able to hit a moving target by any means necessary and show that it is in fact not a paradox. You may use any form of maths as long as it is logical and constrained by current set, number theories.
Clue: you don't need calculus, in fact all you need is periodicity over time, but it might be easier if you use it.
Abstract wrote:Tralix wrote:Solve Zeno's paradox about firing an arrow and never being able to hit a moving target by any means necessary and show that it is in fact not a paradox. You may use any form of maths as long as it is logical and constrained by current set, number theories.
Clue: you don't need calculus, in fact all you need is periodicity over time, but it might be easier if you use it.
Could you explain the problem completley.... so i don't have to look it up... then maybe i can solve it...
If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.[11] – as recounted by Aristotle, Physics VI:9, 239b5
In the arrow paradox (also known as the fletcher's paradox), Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (durationless) instant of time, the arrow is neither moving to where it is, nor to where it is not.[12] It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.
Whereas the first two paradoxes divide space, this paradox starts by dividing time—and not into segments, but into points.[13]
1. Dichotomy paradox: Before an object can travel a given distance d, it must travel a distance d/2. In order to travel d/2, it must travel d/4, etc. Since this sequence goes on forever, it therefore appears that the distance d cannot be traveled.
Silhouette wrote:
Tralix wrote:Ok just cutting and pasting what is written on the wiki is not an answer.
It's technically correct though.
Silhouette wrote:Tralix wrote:Ok just cutting and pasting what is written on the wiki is not an answer.
It's technically correct though.
Er... I didn't?
And... ok - it doesn't feel like I solved anything though, I just picked out and criticised the main assumption.
You also said Abstract was right for saying something else, so what was the answer you were looking for?
Tralix wrote:Zeno is basically making a logical error of assuming time and distance are exactly halving in his paradox.
Silhouette wrote:I think you mean an acceptance of simple calculus.
You yourself rightly deny that infinity is defined. So for limits to converge towards a definite answer, this is like saying something finite can result from something infinite.
I forget the outcome of this old thread about whether 0.9(recurring) equalled 1.
A convergent series of 9/10+9/100+9/1000+.... would definitely tend towards 1, but for it to equal 1 requires an intuitive leap rather than a strict and rigorous approach taken forever and ever just to never quite get there.
This intuitive leap is necessary for the acceptance of calculus, which is more of a mindset adopted for things like Zeno's paradox to no longer seem paradoxical, than a solution for it.
The Greek philosopher Zeno considered the problem of summing an infinite series to achieve a finite result, but rejected it as an impossibility: the result was Zeno's paradox. Later, Aristotle proposed a philosophical resolution of the paradox, but the mathematical content was apparently unresolved until taken up by Democritus and then Archimedes. It was through Archimedes's method of exhaustion that an infinite number of progressive subdivisions could be performed to achieve a finite result.[1] Liu Hui independently employed a similar method a few centuries later.[2]
In the 14th century, the earliest examples of the use of Taylor series and closely related methods were given by Madhava of Sangamagrama.[3][4] Though no record of his work survives, writings of later Indian mathematicians suggest that he found a number of special cases of the Taylor series, including those for the trigonometric functions of sine, cosine, tangent, and arctangent. The Kerala school of astronomy and mathematics further expanded his works with various series expansions and rational approximations until the 16th century.
In the 17th century, James Gregory also worked in this area and published several Maclaurin series. It was not until 1715 however that a general method for constructing these series for all functions for which they exist was finally provided by Brook Taylor,[5] after whom the series are now named.
The Maclaurin series was named after Colin Maclaurin, a professor in Edinburgh, who published the special case of the Taylor result in the 18th century.
Tralix wrote:Only because you don't understand the underlying laws of calculus.
Limits are asymptotic they neither denote anything "real" nor are they per se fictions. They are what values can approach but never reach.
Silhouette wrote:Tralix wrote:Only because you don't understand the underlying laws of calculus.
Limits are asymptotic they neither denote anything "real" nor are they per se fictions. They are what values can approach but never reach.
*Don't accept the underlying laws of calculus.
Nothing you've said gets rid of this problem of infinity in calculus. Asymptotes are just an example of what I was talking about that you need to make an intuitive leap to reach. And then you say they're approached but never reached, which is just what I said about convergent series never quite getting there if you take a strict and rigorous approach to them forever and ever...
You can't repeat my argument in order to say it's wrong. Quoting the wiki-history of the Taylor series doesn't prove anything either.
Tralix wrote:It isn't a problem an axiom is not an issue unless you make it one by semantics and then everyone will just think you are a crank.
The problem is solved and successfully disputed according to all science and maths. The fact that you don't understand it, is possibly interesting but not a reason to really discuss your ignorance with you.
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