Refuting the counters to Zeno's paradox

[devogue]

No, your reasoning is "mathematical poof".

Turing?

[jamest]

I still see a problem inherent within the utilised symbology and I will be addressing this at some point today.

Promises, promises! Symbols in mathematics are arbitrary, which is the whole idea of basic algebra, but the concepts they stand in for are not. Either the deficiencies in your mathematics education are worse than I thought, or you are pulling our legs with the above feeble attempt at satirical obscurantism; that, of course, may wander into trolling territory if you keep it up for too long.

Let's parse it, though: James "sees" a "problem" in the "symbology". The problem is "inherent" within the "utilised" symbology. Apparently, all this need imply is that an adequate "symbology" would make it all better.

"I will be addressing this at some point today...". A great lecturer hath spoken.

Again, any reasoning here has been directed at a specific mathematical proof.

No, your reasoning is "mathematical poof".

Again, not a single jot of that addresses the meat of any of my posts. Are you not capable of doing so? That's how it seems to me, pal.

[Azathoth]

I counter all these confusing words and numbers thus

[The Dagda]

Before I proceed do you understand the basic rules of integration? If you don't there's little point in me explaining that t and xare related concepts but time halves not distance.

I don't want you to proceed with that. I want you to address my post.

I have

No you haven't. Let's be clear that my reasoning is a response to mathematics already presented - not to any other math. Therefore, if you want to counter my reasoning, then it will have to be in association with that aforementioned math.

the proof relies on the relationship between time and distance it cannot be proven rigidly without mathematics, which actually uses the half life equations to show that at a certain time the amount of distance will be 0.

Philosophically this means that x is infinitely divisable conceptually but in the real world time is not, only so muany things can happen in a time period. This is dealing precisely with your maths without the cumbersome summation notation and it also shows a limit at which the ball comes to rest or the person is struck by the arrow etc.

The integral is a sum of values between a and b, just like summation is. It is the same theorem and it is easilly transefrable to summation by simple steps.

http://en.wikipedia.org/wiki/File:Riema ... rgence.png



This is exactly what you are saying, but in the form of an integral as you get more divisions the solution converges to a point at the limit.

Essentially your assumption that as time halves distance halves is false, because time is finite and distance is potentially only conceptual and is not. If you could take the time to learn how calculus is just dividing up a graph into ever smaller parts just as your summation is adding together ever smaller parts you wouldn't be asking this question at the limit of x because it would be easy to relate real experiment and to see that the smaller the divisions the closer a graph comes to an exact solution of distance over time where x converges.

[jamest]

I counter all these confusing words and numbers thus

Not quite an infinite pair.

[devogue]

I counter all these confusing words and numbers thus

Suddenly it all makes sense.

[the PC apeman]

If the summing of series x is doubtful, then we simply cannot say that x = x.

...which would imply that it is possible that x ≠ x. Is there a mathematics version of the principle of explosion? {A, ~A} thinking is a common hallmark of woo as it allows wooheads to conclude anything they wish.

You're calling me 'a woohead' (more trolling) when you have no rebuttal against my reasoning.

Are you advancing {A, ~A} thinking? If so, you are employing a tactic common among wooheads and I will be glad to rebut it.

Actually, it is Xamonas Chegwé that has apparently applied that reasoning - I just pointed it out. And I've already provided a rebuttal of my own, thankyou.

For the record then, is it your position that it is possible that x ≠ x?

[Surendra Darathy]

Again, not a single jot of that addresses the meat of any of my posts. Are you not capable of doing so? That's how it seems to me, pal.

Here is the "meat" of your posts, James:



It is as if to say that, from its very beginning, your argument was "tits up".

But again, if x cannot be summed, then there is nothing that it is equivalent to. That is, it has no sum and so is not equivalent to anything, most of all the mirror image of its own sum. Thus, essentially, my counter reduces to claiming that there has been an irrational utilisation of the equals (=) sign.

Is this point clear? If not, I'll try to explain it better. Again, I reiterate that this is a point of logic, and has nothing to do with me not understanding the math involved.

The point, of course is that no one is assuming anything about whether or not the sum is defined, i.e., finite. XC used operations on the rational numbers to show that both the original series and its double can be compared termwise across the equal sign.

The only remaining quibble you have is the meaning of the ellipsis (…) in representing the continuation of a series. If the contention is that the ellipsis has no definite meaning in the representation of an infinite series, then you must present the argument for it, straight away, and stop promising that you will get to it "later".

There is a certain use of mathematical induction in doing the termwise operations across the = sign. Your complete rejection of mathematical induction will severely restrict the kinds of conversations you can have with mathematicians.

[Xamonas Chegwé]

Again, not a single jot of that addresses the meat of any of my posts. Are you not capable of doing so? That's how it seems to me, pal.

Here is the "meat" of your posts, James:



It is as if to say that, from its very beginning, your argument was "tits up".

But again, if x cannot be summed, then there is nothing that it is equivalent to. That is, it has no sum and so is not equivalent to anything, most of all the mirror image of its own sum. Thus, essentially, my counter reduces to claiming that there has been an irrational utilisation of the equals (=) sign.

Is this point clear? If not, I'll try to explain it better. Again, I reiterate that this is a point of logic, and has nothing to do with me not understanding the math involved.

The point, of course is that no one is assuming anything about whether or not the sum is defined, i.e., finite. XC used operations on the rational numbers to show that both the original series and its double can be compared termwise across the equal sign.

The only remaining quibble you have is the meaning of the ellipsis (…) in representing the continuation of a series. If the contention is that the ellipsis has no definite meaning in the representation of an infinite series, then you must present the argument for it, straight away, and stop promising that you will get to it "later".

There is a certain use of mathematical induction in doing the termwise operations across the = sign. Your complete rejection of mathematical induction will severely restrict the kinds of conversations you can have with mathematicians.

Thank you SD. You saved me the trouble of pointing out the flaw in Jamest's 'refutation'.

I was very careful never to perform a single operation on the 'sum' as a whole. Every step involved actions on individual terms. That was the whole point in rewriting the proof (at great length, I might add.)

As an aside. The series 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + ... does not converge (it is infinite but approaches infinity extremely slowly) and can be shown not to by using exactly the same terminology. There is nothing in my choice of symbology that presupposes convergence.





Staff hat on.

Nobody in this thread has been trolling. So can we all kindly stop using the word to describe each other. Thanks.

[devogue]

Staff hat on.

Nobody in this thread has been trolling. So can we all kindly stop using the word to describe each other. Thanks.

Can we call each other wankers?

[Comte de Saint-Germain]

Staff hat on.

Nobody in this thread has been trolling. So can we all kindly stop using the word to describe each other. Thanks.

Can we call each other wankers?

Wanker.

Anyway, I'm quite impressed by this thread. It seems there are a couple of people* here with a very profound insight in mathematics. My hat off to you gentlemen!

*No Jamest, not you.

[FedUpWithFaith]

[jamest]

Here is the "meat" of your posts, James:



It is as if to say that, from its very beginning, your argument was "tits up".

Staff hat on.

Nobody in this thread has been trolling. So can we all kindly stop using the word to describe each other. Thanks.

I'll respond to the serious stuff later.

[Xamonas Chegwé]

Here is the "meat" of your posts, James:



It is as if to say that, from its very beginning, your argument was "tits up".

Staff hat on.

Nobody in this thread has been trolling. So can we all kindly stop using the word to describe each other. Thanks.

I'll respond to the serious stuff later.

If posting tits counts as trolling, we are all trolls.


Now come up with something that does some real refuting. We are all waiting eagerly.

[colubridae]

Nice tits... needs some cheeeese.


xeno was he the brother of xena warrior princess.

Better luck refuting her, jamest...