Magnus Anderson wrote:Silhouette wrote:I criticised the use of "infinite" in reference to sets when any aspect of their construction is a product of finitude.

What does it mean to say that an aspect of a construction of some set is a product of finitude?

Take a standard infinite sum \(\sum_{n=0}^\infty{a_n}\)

The start of the sum is defined as 0.

The function "a" is defined and its relation to the starting point is defined by its subscript of n.

The big Sigma defines what we're doing to each term in the series in relation to the others.

All these specified finite constraints are set up using finite notations of finite quantities.

They all come together in one standard construction.

And there's 1 notation that is of an infinite.

All these finite aspects to this construction, and there is 1 aspect to this construction that is infinite.

The finite aspects of this construction are a product of finitude. The infinite aspect is a product of infinitude.

That's what I mean.

Magnus Anderson wrote:Silhouette wrote:I mentioned how even the natural numbers have a finite starting point on the number line

The set of natural numbers does not have a starting point. There is no first element, member, number.

Wow.

Again you distract away from the "well-ordering" of the number line that I was talking about to this less precise "set of natural numbers" with cardinality only.

So dishonest/ignorant. You pick.

Magnus Anderson wrote:Silhouette wrote:never mind the line being finitely bounded in all other dimensions as well

How is the set of natural numbers (not the number line) bounded in all other dimensions?

This is obvious and something I've explained many times.

No doubt you're denying its existence by denying the well-orderedness of natural numbers.

Again you're distracting from my point about the number line just to evade addressing yet another one of the many flaws in your line of reasoning.

Magnus Anderson wrote:Silhouette wrote:being infinite in only one dimension in one direction

How can sets be infinite in more than one dimension and in more than one direction?

Easily.

See how the well-ordered number line of natural numbers doesn't go "backwards" from 1, and it only goes "forwards"? And it only goes forwards along 1 dimension? Perhaps horizontal, like the x axis, or maybe even vertical, like the y axis if that's more convenient: the line goes along only one dimension either way. This is one direction along one dimension only, and starting from the finite quantity of 1. That 1 is a finite constraint on the start. The direction of the progression of the number line is a finite constraint on it progressing along any other dimension than the line it follows. The only thing that's infinite about it is the fact that once it starts, it keeps going in that one direction along that one dimension indefinitely.

How can you not understand this?

Magnus Anderson wrote:Silhouette wrote:It's finite in many more ways than it is infinite, yet it's still called infinite because it's infinite in at least one way.

There is only one way that sets (including the set of natural numbers) can be finite or infinite.

Yes. That's what I've been saying this whole time.

Magnus Anderson wrote:Silhouette wrote:In other words, any size of "infinite sets" is determined by their relative lack of finite constraints and not any "different size of infinity".

What does it mean that sets have "finite constraints"?

See above ^

Magnus Anderson wrote:Silhouette wrote:It's only if you could remove all finite constraints to "infinite" sets, that you'd get an entirely infinite set, which would mean "boundless in every way one can think of".

A set is said to be entirely infinite if the number of its elements is endless. That's what it means for a set to be entirely infinite. A set cannot be more or less infinite. It cannot be partially infinite. It's either infinite or it is not.

A set cannot be more or less infinite!!!!!!!!!!!!!!!!!!

You just said it!!!! THANK YOU.

Thank god this fucking joke of a topic is over on "sizes" of infinity.

obsrvr524 wrote:Silhouette wrote:Principia Mathematica by Alfred North Whitehead and Bertrand Russell.

Building up the foundations of maths, they finally reach 1+1=2 by page 362 (in the 2nd addition at least, in the 1st addition it's page 379).

So you are telling us that someone took 362 pages just to prove that 1+1=2?

First, I don't believe it. And then if they did they were definitely missing something upstairs.

You think that Bertrand Russell was missing something upstairs...

Talk about the fallacy of personal incredulity, guys!!!!!!

Oh wow...

You two guys...

obsrvr524 wrote:Silhouette wrote:Goddamnit, why is it so impossible for amateurs to believe that someone else might know things they don't?

Dunning Kruger effect, obviously. But fuck me is it frustrating to have to deal with.

I realize that appearances aren't everything and no offense but compared to Magnus, you are the one who appears to be the amateur here suffering from Dunning-Kruger effect.

As he pointed out earlier, you have not shown any flaw in his argument. You just say he is wrong and then give your own narrative. If Whitehead and Russel argue like that, I can see why it took so long for them to do so little.

Sure I do, mate Our previous encounters on infinity make so much more sense now you've revealed your ignorance about Russell and mathematics.

What are you doing on a philosophy board again?

Fair play if you actually want to learn from your lesser positioning, but all this time you've actually been professing expertise and credibility just like Magnus - the other charlatan of the same kind. Oh internet..., how do you manage to bring out the quacks so efficiently and effectively?

I have thoroughly shown very many flaws in all arguments against \(1=0.\dot(9)\) and all the other peripheral arguments brought up around that position.

Now that you've revealed you have negligible background or capability on this kind of subject, my suspicions have been confirmed that it is likely sufficient to regard your opinions on my reasoning about it as null and void.

Magnus Anderson wrote:Here it is:

\(\frac{9 + 0.\dot9}{10}=0.\dot9 + \underline{\text{the missing term}}\)

If you're asking me about its value, I don't know, I didn't calculate it. Do you really think such is necessary in order to prove that there is indeed a missing term? I don't think so.

Well how about you fucking calculate it, eh? Magnus?

Come back to me when you actually have something, huh?

Magnus Anderson wrote:What do you get when you take \(1 + 1 + 1 + \dotso\) and add one more term to it? You get \((1 + 1 + 1 + \dotso) + \underline{1}\). The underlined is the added term. That's where it is. In this particular case, it's pretty easy to calculate the value of the added term because every term in the infinite sum \(1 + 1 + 1 + \dotso\) is equal to every other. This isn't the case with \(0.\dot9\), so figuring out the value of a single term is not so straightforward. You'd have to find an equivalent infinite sum where every term is equal to every other and then calculate how many terms of that sum is equal to a single term of \(0.\dot9\)

So add 1 to an endless string of 1s. Is that all you have?

Is it "more endless" than "endless" now?

Is the "size" of the number line of natural numbers bigger now?

So basically the extra 1 is nowhere, right? It's nowhere, thats where it is.

Add 1 to any finite set, and sure - you're absolutely perfectly unequivocally correct!

gib wrote:Don't you know about second infinity, Silhouette? Ask Magnus all about it.

MagsJ wrote:Still following..

I will adject when I see fit, but right now my money is still on Magnus, as man’s held his ground and not swayed from his thinking. No pressure though bro, ok? lol

Yay, the opinion of someone who puts money on stubbornness and neither learning nor adapting anything.

Thanks for your reliable non-contributions, MagsJ.