Strange

Which is a common (informal) proof that you can't do arithmetic using infinity. So your ω + 1 or ω-1 doesn't make sense. We can probably all agree on that. As I say, take some time to think about where the problem might be.

You will need to present your proof here.

I found out on another forum when one of the moderators went rogue!

@Edgard Neuman Several people here think you are wrong. You are disagreeing with some of the greatest mathematicians who have ever lived. Have you ever stopped for a moment to consider that the problem might be with your understanding?

That is not possible. You said that w = Card(N). Card(N)-1 is not in N. It doesn't contradict (2) because ω-1 = ω (if it is defined at all) The problem with your argument is that you say there is an integer (ω-1) in N such that adding 1 is no longer in N. Firstly, this contradicts the definition of integers (every integer has a successor) but it also says there is a largest integer. Please tell us what the value of this largest integer is. And then why you can't just add 1 to it.

Neither (ω-1) * 2 nor (ω-1) are in N. So this is not relevant.

It disproves your arguments about there being integers that are not in N (or whatever nonsense you are claiming). This is not an assumption, it is the definition. We know Card(N) is infinite because it is larger than any n in N. Correct. Because you can't do integer arithmetic on infinity. It is not, as you said before, a sequential operation. So this is a bogus argument.

This is painful. You ignored this: It is up to YOU to prove that there is a maximum integer in N.

This is true by definition: every integer has a successor and so the series is unlimited.

You have ignored the most important part of that post. The part that will prove your argument wrong.

OK. So answer Carrock's post above, then.

Every n is in N but Card(N) is not an n. So your argument fails.

You might be relieved to know that us mere mortals can't ignore mods. Much as we might like to!

So what. How is that relevant?

OK. So Card(N)-1 and (Card(N)-1)*2 don't really mean anything because Card(N) is not an integer.

What is N in this notation? This statement doesn't seem to make much sense, perhaps if you define what N is, it might make some sense. Edit: Is N supposed to the set of natural numbers? If so then the cardinality of N is infinity and so is Card(N)-1. And so is (Card(N)-1) * 2 But you are right that NONE of the these are integers. But that doesn't seem relevant to anything you have said before. You don't seem to understand the concept of infinity. The reason nobody believes you is because you don't know what you are talking about. Study mathematics?

Huh? If A is the set ofall integers, then it contains all the integers multiplied by 2, therefore it contains B. So you are saying that the result of multiplying an integer by 2 is not an integer? Obviously nonsense. You seem to be the one who thinks it is a recursive process. You don't have to "reach" all because it is not a recursive process. So if we make a statement about all integers then it is true for all integers. Yes you can. The hotel may be full but you can still add an infinite number of new guests. This is at the heart of your error. Really?

A number with n digits must be larger than N. So your number 10…101010 representing the set of even numbers is not in the set of natural numbers and so needs to be added. Repeat ad infinitum to prove that the set of natural numbers is infinite and the number N does not exist.

And, what is still being ignored is that the definition of "perfect" is subjective and context dependent. So it is not surprising that one can create a paradox by choosing mutually contradictory definitions. That says absolutely nothing about other people's different definitions of "perfect".

They are the same thing. When you walk 3 metres from your chair to the door, that distance is not an "actual thing" (depending, of course, on what you mean by "actual thing"). And that distance is exactly that is being measured and used in the description of motion etc. I don't think it is misleading. Although it might be more accurate to say that it is the geometry that relates our measurements that changes. But as those measurements are what define "space" and "time" (and their relationship) it is pretty much the same as saying that space-time is curved. It is mass that curves space and time; one of the effects of that is the gravitational lensing of light around the Sun. Another effect is the apparent force that we call "gravity".

So you think the Gospels are “Merely corroborative detail, intended to give artistic verisimilitude to an otherwise bald and unconvincing narrative” as WS Gilbert put it.

If you are thinking of the recent set of posts on rockets (and similar posts in the past by the same person under multiple names) then I assume they are deliberately trolling. (I did wonder about the "very young" option that DrP suggests, but I would expect more engagement in that case. Maybe very young and autistic? But it doesn't "feel" like the right explanation - we have plenty of members on the autistic spectrum who engage well in discussions.) If people are serious but ask a question that is too brief, then the only solution is to ask for more details or clarification. That usually works, although some people don't find it easy to organise their thoughts well to ask good questions, so it can take some iterations to get to what they are really asking (a background in customer support helps!) People who post too much are often a bigger problem. Trying to get them to précis or even identify the key point can just lead to another equally long screed. Related: I used to be a member of Stack Exchange and answered lots of questions there. But I got fed up with the non-stop snobbery about "the wrong sort of question" or "questions that attract the wrong sort of answer" and so I deleted my account. If you think down-votes are a problem here, they are like a disease on Stack Exchange!

That cannot be the correct definition of "perfect" for a prey animal. By definition, a prey animal exists to be eaten. Therefore a "perfect" gazelle is one that can be caught, but escapes often enough to allow the species to survive. I think that both Creationists and evolutionary theory would agree about that. Although, a "perfect" prey animal according to Creationists should be one that just appears from nowhere, rooted to the spot, when a predator was hungry. There would be an inexhaustible supply of these magic animals so lions would never go hungry. But not so many that they would get fat. Also, a "perfect" mosquito wouldn't carry malaria and their bites wouldn't itch.

Are you absolutely certain that your definition of "perfect" for gazelles and lions is the same one that Darwin had in mind? Or that Creationists have in mind? Do you have a reference for Creationists defining "perfect gazelle" in this way?

There seem to be a suspicious number of first posts that slip in "acquired from br***r" where it doesn't seem relevant, and then don't engage in discussion. Some of the same posters have had spam links removed. So I assume this repeated plugging of "br***r" is some sort of low-level spam advertising campaign. Edit: Damn! And I have just reinforced it!