MoK

Yes and thanks.

Thanks for the clarification. Can we calculate the contribution of the \omegath term to the series?

It is alright guys. I learned lots of things from both of you and I am thankful for it. I don't think that personal attacks are useful though when peo...

@"fishery" already explained how to resolve the problem of indexing here.

Do you mind elaborating?

Thanks. So you simply extend the natural number to the extended natural number and resolve the problem of indexing.

That is an infinite sequence. I am however interested in the sequence first mentioned by Zeno in Dichotomy Paradox in which the infinite member exists...

Please accept my apology. My, argument here was for Dichotomy paradox. You need to replace the arrow in that post with the runner, Atalanta.

Thanks for the correction.

I mean you cannot give indexes to all members of an infinite series.

I can define the speed in ith step as follows: v_i=\frac{(\Delta x)_i}{(\Delta t)_i} where (\Delta x)_i is the length of ith interval and (\Delta t)_i...

Continuum is a continuous series. He understands what continuous is if he understands what continuum is. Thanks. @"fishery" gave a definition for a co...

I am not sure whether he was familiar with the concept of speed or not. But, the average speed in the interval i can be calculated as v_i=\frac{(\Delt...

Could you calculate the speed in all infinite steps?

If by dense you mean that there exists a point between two arbitrary points then I understand that applies to the set of rational numbers. The link yo...

How could you index an infinite set of steps?

Well, if space is continuous then it means an infinite number of steps exists yet we cannot complete them. The same applies to time in the example of ...

I want to say that you could sweep all points of the continuum using that definition.

He asked for a definition of continuous and discrete in plain English. Could you please provide the definition in plain language without referring him...

Ok, I see what you mean and I agree.

You are talking about physical objects that have extensions in space so their location is not definable unless you talk about their center of mass. Do...

What about the conclusion that spacetime is discrete? Yes, weather forecast for example. Any chaotic system in general. Even nonchaotic systems show t...

Correct. So we are on the same page. Isn't the set of steps the set of physical steps? If yes why do you use a one-to-one map? I cannot figure out wha...

Correct. How about considering the point between two arbitrary points, namely a and b, to be mean, namely (a+b)/2? If not, could you please define the...

Yes, it has an implication. I think it means that spacetime is discrete.

There are an infinite number of steps but we cannot complete them. The fact that we cannot complete the steps does not mean that they do not exist.

Consider a set of points. We say that the set is continuous if there is a point between any arbitrary pair of points. We say that the set is discrete ...

Yes, if the spacetime is continuous and we treat it as discrete then we are introducing error. If spacetime is discrete we introduce error by treating...

That is not a solution but the point of Zeno. If the final step is logically impossible then you cannot complete an infinite series of finite steps th...

I think if spacetime is discrete and our capacity to measure spacetime interval is much higher than Planck length and time then we can treat spacetime...

What is your solution to the paradox? Could you explain @"sime"'s solution to me?

Exactly right! So what are the options in this situation: (1) Spacetime is discrete or (2) Spacetime is continuous. In the first case, we don't have t...

Thank you very much for your post. Unfortunately, my country is under sanction and I cannot purchase any book from Amazon. I am retired and living in ...

That paradox is nothing more than Zeno's paradox. It simply replaces the distance in Zeno's paradox by time. There is however a problem when you want ...

There is no paradox there. The total time which is needed to get to the top is 60 seconds. You might find this link useful.

You can find all sorts of people in any forum. I agree that the number of knowledgeable individuals may vary from one forum to another. That is all ri...

I have to disagree. I have a wide range of interests. One of the main reasons that I signed up in this forum was the very good quality of knowledge of...

Ok, I will try to get the book you suggested in this thread.

If your question is whether spacetime is continuous then I have to say that there is an ongoing debate on the topic. I am not an expert on the topics ...

Thanks for the writing. I will see if I can find any time in the future to study the filter. I have other interests as well rather than mathematics.

Ok, thanks for the clarification.

Thanks for writing. On my reading schedule.

Again, thank you very much for providing the argument and extensive writing. I will read through the argument and try to understand it. I will look fo...

I didn't ask for a proof that shows that aleph_0 is the least infinity but to show that X is the least infinity namely aleph_0.

A mistake on my part and I am sorry for that. I should have written: "To avoid confusion, assume that the cardinality of the set of natural (I wrote r...

Ok, that I agree. How about whether the real number represents reality or not? Do you know any references that claim that reality is not continuous? I...

I am aware of that. To avoid confusion, assume that the cardinality of the set of real numbers is X. How could one show that X is the least infinity n...

I directly attacked the continuum in the mathematical sense. The discussion is ongoing but it seems that the classical continuum exists but suffers fr...

Please accept my sincere apology for not replying to your post earlier. I read your post a few times in the past and had a difficult time understandin...

What do you mean by this? Do you mean that the set of natural numbers is the set of aleph_0? aleph_0 is a number. How could you treat it as a set? I d...