You are just talking about a continuous number line, which is actually a requirement for the FTC. The curve must be continuous from a to b.

But yet it is not impossible to sum them, which is what we are concerned with.

Yes it does, this distance from Achilles to the Turtle is finite, even after accounting for the movement of the Turtle. The only thing Zeno's paradox does is create an infinite number of points on a finite number line.

I am not concerned with the parts as the parts are infinite, that is not the point, I am interested in the sum of the parts which is finite.

We I get done with work, I can do up a visual I think which may help.

Calculus is about net change, so we'd be looking for the net change from 0 to 1. You can put that on a number line call it F(b) - F(a) and you have the Fundamental Theorem of Calculus.

Sure it does, Zeno's paradox is about getting from point a (the start of the race) to point b (the turtle) over infinite small intermediate distances. This is exactly what calculus is.

The track of land is basically an arc length and we are looking for the net change from point a to point b. That's calculus.

Sometimes it is good to revisit the classics.

Zeno's paradox in mathematics lends to the idea of infinite partial sums, which is the sum of infinite parts. While it can be divided an infinite number of times, it still sums up to a whole, hence we can cross the room. I am not sure how that fits in with supertask, but even if we decide Zeno's paradox is wrong, as clearly we can cross the room, it still highlights important mathematical concepts.

Yes, I know you are eager to put me in place because you don't like me.

This is actually sequences and series that leads to an important mathematical concept that I studied in the college classroom and was tested on. Did you take those classes? Did you read the book? Here the answer is in this book. . .

https://www.amazon.com/Calculus-Early-Transcendentals-MultiVariable-Rogawski/dp/1464171750/ref=pd_lpo_sbs_14_img_0?_encoding=UTF8&psc=1&refRID=V13FMHA65YWJKE428B0F

That is essentially what you are doing, it is something people do when they don't want to have an actual discussion but they want to claim someone is wrong. If it helps focus on the fractions and forget we are talking about length.

Try to think of it this way:

I want to cross 10 meters but to do so first I have to get to the half way point.

10/2 = 5

Then I have to get to the half way point of 5 meters.

5/2 = 2.5

And so on.

2.5/2 = 1.25

1.25/2 = 0.625

0.625/2 = 0.3125

0.3125/2 = 0.15625

0.15625/2 = 0.078125

etc....

That will go on forever, it is called a series.

In theory length is not discrete, only our ability to measure it is.

It is a very important paradox concerning series and calculus. Ask yourself: How is that you can have an infinite number of distances to cover, but yet still be able to cross the room?

I think it is time for a new conundrum, something easier. I have one in mind, I just hope it is not too easy.

If 0% was in the OP we would have lost that entire part of the discussion.

People want to wrap this question up in a nice bow, with everything in its place, that's why some think 0% should be C), as they think it makes it nice and tidy.

Some want an answer, even though the question, which does have an answer, can't be answered. That is where the 33% comes in, they need it to have a best answer. It is human nature, to try and put everything in its place even if it has no place; we are the diligent organizers of an endless chaos.

However, to get to those points they must redefine the question; they must change the question. As if they are trying to avoid the original question, because it messes with their human nature.

The question as it is in the OP is the best version if it, as it is nonsensical chaos on more levels than one, which is the point. It is a reminder that these systems we have built, like mathematics, are not perfect and they only work up to a point. It is a reminder that for all our great insights, our understanding of even our own concepts is incomplete.

What is see is people doing what people tend to do: Unnecessarily over complicate things. It is why the Law of Parsimony exist, to help mitigate such observational bias.

I see you creating an entire narrative, a fantasy world, to try and facilitate your position. It is on a test, it is being graded, there is an instructor, there are students, etc. . .

Not only are you making a ton of assumptions about the nature of all these fictional story elements, but you are taking the OP out of context.

I find it interesting that the three sample space notion requires more hoops to jump through than the four sample space. That's why people feel the need for these out of context examples; they have to redefine the question.

Can we say Occam's Razor?

Anyone else want to back the horse that the second 25% was put there by mistake? Or can we all at least agree the question was purposely designed with it?

This is not a test and clearly the second 25% is meant to be there.

It was not a mistake the question has two 25% and one 50%, with four possible answers. That very much seems to "imply" a sample space of four.

The second 25% is clearly intentional and not a typo.

I already know your argument, Michael. Unless you are repeating yourself for someone else?

My position has not changed, despite your renewed effort.

Listen, as I told Michael, my entire arumgent is on the table, and I have repeated myself many times already. It is all there just go read it. Also don't confuse the word logical with the word reasonable.

Because my arumgent is sound, besides I hate it when everyone sits around agreeing with each other, it is incredibly unproductive.

Implied?

That has observational bias all over it. That is the difference that you are not seeing, I am not reinterpreting the question.

You don't just remove observations to fit your answer, that is called data hacking and as far as I am concerned, we are analyzing a data set with four observations, so you need a damn good reason to just drop one.

Not one person gave a valid reason for dropping a datum.

Let's hear your logical proof for dropping a datum.

Taking things out of context, doesn't prove you are right, it just proves that you can't read.

I actually made several points, but the one that got everyone hopping is that with the sample space in the OP you get a distribution which favors 25%. The entire conversation is recorded if you wish to review it and if I thought it was incorrect then I won't assert it as correct, would I?

I'll keep my thoughts to myself.

Feel free to actually address my argument, as far as I can tell you only joined this conversation to poke at me.

The conversation would have never got this far without my input. Don't like me fine, but no one has actually proven me wrong and my argument is a very valid take. I am an ass, yes, but I am also smart and you'd be fooling yourself thinking otherwise.

I don't think it is unreasonable of me to ask that we focus on the question in the OP and your aversion to do so is very suspicious. I also don't think these rapid fire replies do anything at all, I know from experience that they tend to lead nowhere.

Now, Michael, I have already said my part on this, and I do fully understand what you are saying, so unless you are going to bring a new argument to the table, then that I think this is it. I will continue to think you are just flat out wrong, that part will not change but unless you can provide some new perspective here, then there is no point for me to continue in this. The only thing that will happen is at some point I will insult you and I'll end up getting more post deleted and more messages in my inbox from mods.

You seem to want to have this conversation with me, so I would say it is very relevant.

I don't care about Paris, Michael, it is you trying to stack the deck.