Is 1 = 0.999... ? Really?

It’s important to note that you’re using known words in a way other people don’t.

Normally, a set is said to be infinite if and only if it contains a number of elements greater than every integer. That’s it. Thus, both ({1, 2, 3, \dotso}) and ({2, 3, 4, \dotso}) are infinite because the cardinality of both sets is greater than every integer. That one is greater than the other is irrelevant.

Also, the distinction between your “infinite” and your “semi-infinite” isn’t entirely clear. (The relevance of that distinction isn’t clear either but let’s ignore that for now.) If the set of all numbers is “infinite”, what is the set of all numbers and all letters given that it’s bigger?

In the English language that means that both are infinite (or “endless”). Saying that a set is infinite is merely saying that it has no last element.

We don’t have a problem with you calling some of them “semi-infinite” - meaning that the set is less than the set of all integers. We don’t see why you want to say that but it’s logically ok.

But that is not really ok.

First “infinity” isn’t a quantity. “Infinity” means the first step beyond the endless. It is a target to aim for. But it is not on the map. No set ever reaches or encompasses infinity.

But also there is the issue of having more than one completely infinite set (set of all A1, A2, A3… and the set of all B1, B2, B3…). Combined infinite sets have more than merely one infinite set (obviously). And there is no limit as to how many infinite sets can be combined so there is no “infinity”.

That is all merely semantics after you invented a word. But why do we care?

There are obviously sets that are more than merely the infinite set of integers. That is why James defined his “(InfA)” - to distinguish the set of all integers (or naturals) from any shorter or longer set. Your “set B” above would be (InfA-1).

It may be that the set of all numbers is not infinity because we have to account for the set of all letters as well. Where we have to do this, then the set of all numbers is a semi-infinite to me. To me, if it can be greater in size, then it is not infinite. Infinity = the set of all things. Infinity = that which is omnipresent. Nothing is greater than this in size.

Since you do not call air on our planet as being omnipresent (there is no air in space, therefore air is not omnipresent), consistency would have you not call that which can be greater in size as being infinite. Thus anything other than Existence or the omnipresent, or the set of all things/existents, is non-infinite and non-omnipresent in my opinion.

Since we do not call air on our planet as being omnipresent (there is no air in space, therefore air is not omnipresent), consistency would have us not call that which can be greater in size as being infinite. Thus, anything other than Existence or the omnipresent, or the set of all things/existents, is non-infinite and non-omnipresent in my opinion. I’m taking an absolute approach regarding this matter. By this I mean if it’s not perfectly/truly triangular then I would call it a semi-triangle. Similarly, if it’s not truly omnipresent or infinite, then I would call it semi-omnipresent or semi-infinite.

I think it is a quantity. I see infinity as the quantity which encompasses all semi-infinites and finites. When you put infinity into the same class as semi-infinities, you end up with an inadequacy. You could say there are many infinites and the biggest one encompasses all the smaller ones, but I prefer to say there are many semi-infinities and finites, and they are all encompassed by infinity.

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Because it addresses semantical inconsistencies I believe to be present today in maths.

Call the set of all things/existents V. Call the quantity of all things/existents infinity. Call any quantity that is not finite or infinite: semi-infinite. You can account for all semi-infinites in this way (of which there will be an endless number of, and all of which are encompassed by V or infinity). Take infinity out of the equation, and it’s like you have no all-encompassing quantity (which to me, is madness. Yet, to my understanding, currently maths is like this. As in it has no all-encompassing quantity).

So you are just making up your own definitions for existing already defined words.

And you expect that to cause anyone to believe in God? :confused:

It is confusing to say that infinity is a set if at the same time you’re claiming that it is a quantity. You might want to say that infinity is a number equal to the number of elements contained within the set of all things (albeit the concept of a set of all things isn’t entirely clear and requires further clarification.)

If there is no quantity greater than infinity then what you mean by infinity is perhaps “the largest number”. That, however, would raise the question whether the cardinality of the set of all things is equal to this number.

Ultimately, your definition of infinity is non-standard and I don’t see why we should adopt it. More importantly, I don’t see how any of this answers the question posed in the OP. It looks very much off-topic.

“The largest number” isn’t anywhere close to being the largest quantity. That is what the Cantor set theories were about. That is how we got cardinalities. And as Cantor stated - “there can be no highest cardinality” - no largest quantity.

You might want to consider presenting an argument in favor of that claim but somewhere else (:

Right now, I am trying to understand Certainly real’s claims. Though, it might be better for me to first do a check on whether what he’s saying is relevant to this thread or not. So far, it does not seem to be the case.

It is a discussion about infinity but it really does belong on one of his threads.

I gave my reasoning for why I distinguish between the semi-infinite and the infinite. If someone wants to make a distinction between these two semantics by calling one infinite whilst calling the other truly infinite, that’s also fine in my opinion. But when no distinction is made between the truly infinite and that which is not truly infinite, then I think confusion can occur.

Existence is the set of all existents. It is also a meaning. It is also an existent. Its quantitative capacity is infinite, and by this I mean, the quantity of things it encompasses is infinite. So as a set it encompasses an infinity of things, hence why it semantically qualifies as being the infinite set, and why it is also a number. Alternatively you can put it this way:

Infinity = a number
The infinite set = the set that encompasses an infinity of things (the set of all sets: Existence).

Yes I think that’s what I meant. Maybe I should say the set of all existents instead of the set of all sets. But they both amount to the same thing. Existence, the infinite set. The universal set.

Yes, I see it as the largest number. And yes, I see the cardinality of the set of all things as being equal to infinity.

To be fair, I did not focus on the OP beyond the fact that it is about infinity. So to that end, I will stop discussing infinity and semi-infinity here.

Infinity is not a noun. It’s a verb. It’s a process. If infinity were a thing it’d have borders.

CR,

Your need for god to exist is clouding your judgement.

Who are you talking to? If you’re talking to me, you are needlessly repeating yourself. That’s not welcome.

I see.

Whether it should be a noun or not - whether their definition is precise or not - is totally irrelevant to the fact that in English “infinity” is a noun.

Actually, proofs are made through definitional logic that is self evident.

Since the computer doesn’t know what self evident is, it runs in vague circles.

Ask the computer if it is ambiguous for beings whether their consent is being violated in a visceral manner… (self evident to each being)

There are also inferential proofs, say, the counting numbers… even though we can’t count them all, we still know it’s a well ordered set through deduction and inferential proof (we infer evident proofs)

lol @ the consent stuff

That is pretty fucking funny.

The math stuff was gibberish too.

It literally tried to explain infinitely adding 3 to something forever and gave this as an example:

2+1=3, 2+2=4

This AI has been short circuited many times now.

That isn’t what it was doing. It only said 3 because it started with that and then immediately went to four. It was just writing an infinite series while talking about sets

" 3= 1+2… 4=2+2" [You can continue it: 5=3 + 2, 6= 3+3, etc)
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1 and 2 does make 3, you know that right? 2 and 2 do make four. So it was correct…

So how was it short circuited?
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I already said it!!!

Before it added that set, it set up its example as adding 3 forever …

That example has NOTHING to do with adding 3 forever!!!

It short circuited.

It doesn’t know what it’s talking about.

Everyone knows what an inferential well ordered set means, even if they don’t know the TERM.

The part where the machine stated something like “that’s besides the point” was actually the WHOLE point.

Again, a malfunction.