Is 1 = 0.999... ? Really?

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? :smiley: lol

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.

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.

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.

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?

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

See above ^

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.

You think that Bertrand Russell was missing something upstairs…

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

Oh wow…

You two guys…

Sure I do, mate :slight_smile: 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.

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

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

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!

:laughing:

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

Thanks for your reliable non-contributions, MagsJ.

That’s true but it’s trivial and irrelevant.

That’s also true and it’s also trivial and it’s also irrelevant.

Here you say that there are things that defy definitions which means that there are things that cannot be defined.

But it’s not things that we want to symbolize that we define but our symbols. To define some symbol S is to verbally (or non-verbally) describe its meaning.

If you want to say that there are things that cannot be represented by symbols, that’s a different story, but you’re still wrong. Anything can be represented using any kind of symbol. All it takes is to pick a symbol and say “This symbol represents that thing”.

If all you want to say is that the symbol and the symbolized are two different things, fine, but 1) you’re using way too many words, and 2) I don’t understand the relevance of that.

You’re also claiming that the act of defining words is questionable.

We’re supposed to believe that there is something questionable about the act of using a finite symbol (such as a word) to represent something that is infinite.

And here’s more of your obscurantism:

You’re speaking of concessions, definitions that are merely apparent, the idea that finitude is synonymous with definability and so on.

You’re asking for more proof than necessary.

Then be more succinct, and then I/we may take more note, but until then…?

May I ask… why do you always feel cornered/hounded? I’m very observant you know. ; )

Oh I contribute plenty! but you’ll never know… coz I never tell. :-$

I’m tired, so will re-engage on this later.

Isn’t it simple logic to deduce that you have a pattern that isn’t going to change as you proceed toward infinity? Doesn’t calculus do that at its core?

Every item need not be individually counted just as every item need not be printed out. A series is deducible. And a process is deducible, else the sum of convergent series could never be known.

Now that was an example of pointing out a flaw in the other person’s argument. When is someone going to point out a flaw in Magnus’ argument?

That’s precisely the point: to distract you from your own distractions.

Noone here is as preoccupied with their self-image as much as you are.

As for calculus, like I stated earlier, it’s a ROUNDING discipline.

When people enter the shitter is to declare an equality for the sequence and call it a “bound infinity”

I agree Magnus wins the stamina race.

He also wins the ignoring people race.

I ask him point black, what’s 1/2 infinity… ? he cowers.

The reason he cowers is because of two reasons:

1/2 infinity means nothing. The second reason is because it makes it nonsense to talk about two infinities, they are merely (2) 1/2 infinities, which still only equals a whole infinity.

Magnus needs to be able to say that 2 infinities exist to keep going with the thread…

It’s absolutely relevant since the core of your argument is to regard the infinite as finite.

I say there is a problem with this.
You agree that words aren’t what they represent.
The definite symbol (\infty) is not definable - it represents the exact opposite of definable even though the word/symbol/signifier takes the same form as things that are definable.
See, you agree with me and understand the undeniable logic that I’m forwarding but you won’t lend this your slightest acknowledgement. So dishonest.

The act of definining words is questionable by virtue of words not equalling what they represent, which is the source of many philosophical misunderstandings and is solved by Experientialism - but this more general concept is beyond the scope of this thread, although the specific instance of a finite symbol representing an infinite quantity is absolutely central to the thread and your misunderstanding of “infinity” as finite.

I’m not saying you can’t pretend that the symbol (\infty) can be used to signify infinity - clearly it routinely is - but the superficial appearance of a signifier must not be confused with the nature of what it denotes when the nature of the signified is that which defies symbolic representation.

My whole point this whole time is that while you can write (\infty+1) etc. and everyone knows that you think you mean by this, the inherent problem of defining the symbol of undefinability completely nullifies the sense we can make of (\infty+1).

You’re not describing the meaning of infinity by symbolising it as (\infty+1), you’re inviting the possibility of a whirlwind of misunderstanding. “I picked a symbol to represent that which can’t be summed up in a symbol” does not make for a sound foundation. Admit this, and the impending chaos that it inflicts on your points.

Let me know in all honesty if you think finitude is at odds with definability.

This will give everyone a very clear indication of how competent you are with semantics: a context with which we can frame this entire debacle such that we may mentally resolve it with immediate finitude.

Funny, because I already denied any involvement in the already-established and legitimately accepted proof that (1=0.\dot9) and encouraged you all to forget I had any part to play in the fact that it’s already been proven by professional mathematicians. I don’t want any credit nor hope for any personal gain from the success of people learning why something basic is true.

I give no shits about what you or anyone thinks of me, I post here solely as an exercise to familiarise myself with the kinds of bullshit that irrational and amateur people come up with against good ideas - and even hold open the possibility that they might have thought of something that I haven’t in coming up with my own ideas. This is a testing space for me, I don’t want friends or respect, but I do respect people who have the intellectual fortitude to recognise closure when it confronts them. I naively hope that this will happen, and sometimes it does, and even though I expect average people to be intellectually deficient I so far have not mastered the ability to refrain from frustration when they inflict their weaknesses upon me. Maybe I’ll overcome this weakness of mine one day, but I’m still not fully sure that I need to.

Yeah.
It’s not necessary to prove the crux of your argument.
You’re right… :icon-rolleyes:

Succinct replies leave too much to the imagination and satisfy the impatient pleasure principle more than intellectual rigor - I require that subjects are sufficiently and exhaustively dealt with. Brevity is a secondary aim, but it is limited by the degree to which I demand thorough dealings.

I rarely feel cornered, and have not been so far during this thread so your observation skills have unfortunately been mistaken.
If you felt as though I was, then regretably you have misjudged my comprehensiveness as corneredness though you have correctly identified my frustration with my feeling of houndedness by the tedious repetition of falsity.

Yeah yeah, jam tomorrow.
Funny how your excuses are never followed up - I’ll never know the plenty you contribute indeed!

I don’t see how that makes any sense at all. It’s very obvious that the symbol (\infty) certainly is defined and well known (for centuries).

Additionally infinity itself is defined and well known. The only problem that I see is that it is not defined sufficiently for maths operations to be sensibly used on it.

That’s not true. What I’m doing is I’m treating infinite quantities as if they are quantities.

Maybe you should start with the word “definable”. What does it mean? What does it mean to say that something is not definable?

In most cases, there is absolutely no need for symbols to look like what they represent.

The sentence “infinite line of green apples” looks nothing like the infinite line of green apples and it doesn’t have to. (Indeed, it would be a problem if it looked like the infinite line of green apples.)

If the purpose of symbols is to merely represent something, and not to look like that something, then there is absolutely nothing questionable about the act of symbolization. (Cryptography must be a very questionable practice.)

If there’s an infinite line of green apples in front of you and you say “Look, there’s an infinite line of green apples in front me!” the statement isn’t false by virtue of not looking like what it represents. The word “true” does not mean “a symbol that looks exactly like that which it is trying to represent”. It merely means “a symbol that can be used to represent that which it is trying to represent”.

You didn’t explain why.

Here’s the problem. You’re saying that one can only pretend that the symbol (\infty) can be used to represent infinity. But that’s not true. I don’t have to pretend. The symbol (\infty) CAN be used to represent infinity without any sort of pretense.

So I was right when I said that you’re one of those people who think that the symbol must look like the symbolized in order to be able to say that the symbol represents the symbolized. According to you, if the symbol does not look like the symbolized, you can’t say the symbol represents the symbolized, but you can pretend that it does. Useful contradictions and all. Beside being wrong, what you’re doing here is justifying contradictions in the name of utility.

The symbol (\infty) does not represent undefinability. It represents infinity. Infinity and undefinability are two different concepts.

When I use a symbol to represent something (e.g. an infinite line of green applies), I am not describing what that symbol means, I am simply using a symbol to represent that something.

There is absoultely nothing that cannot be represented using a symbol. All it takes is to pick a symbol (you can literally pick anything) and say “This symbol represents this thing”.

The problem is that you do not understand what it means to say that a symbol is representing something. You have this naive idea that to represent something means to find a symbol that looks exactly like that something. That’s not true.

In other words, you think you’re an expert semiotician while in reality you know nothing about semiotics.

They are different concepts.

That merely means you’re one of those people who do not think but merely follow whatever is popular at the time.

You are deferring to the authority precisely because you have no idea why (0.\dot9 = 1).

I am not using the yellow rectangle to shift the purple one. Rather, the purple one is where it is because of the position of its equivalent rectangle (the red one.)

The purple rectangle represents the red one and the yellow one represents the blue one. The blue one and the red one are independent from each other – they have no terms in common.

You have yet to show me my mistake.

The point is that the red rectangle is not (10) times the green rectangle.

Not quite.

They aren’t and you should go back and re-read what I wrote instead of being stubborn.

The word “infinity” does have a definition.

Or maybe it’s the case that you see contradictions when there are none? Perhaps because you do not understand the meaning of words?

Which is completely irrelevant. Just because the limit of an infinite product is (0) does not mean the infinite product itself is (0).

Not sure what it means to say that an infinite line of green apples is “more boundless”. I certainly didn’t say such a thing. I said that the number of apples is greater than before.

Yes, it’s endless. I certainly did not say it’s finite. My point is that the number of apples is greater.

Correct. But something did happen to the number of apples.

“The quality of having no quantity” is your own idiosyncrasy that has nothing to do with the standard definition of the word “infinite”.

Here we go again. One assertion after another, no arguments whatsoever.

What do you think you can achieve by merely restating your beliefs?

Sure, but how are you going to deduce that one set is bigger than the other?

You added a red apple to an infinite line of green apples. It logically follows that you increased the length of the line.

  1. You have an infinite line of green apples in front of you.
  2. You add one red apple at the beginning of the line. The line is otherwise unchanged.
  3. If the number of apples is the same as before, it follows that you didn’t add the red apple (contradicts premise #2) or that you did add the red apple but that some other apple was removed (also contradicts premise #2.)

Where’s the flaw?

Magnus,

I have a story to tell you. I hate last minute appointment changes more than most people. I’m not a very spontaneous person to that regard. But! If I get early warning, I can psychologically prepare for it and be fine.

The reason I told you this story is because you’re going to lose this debate, like I stated earlier, we’re only getting started. You can thank me for the “heads up” later.

————————

So here’s the deal Magnus, your dot argument is a magic trick.

Here’s why.

One set: 1,2,3,4,5,6,7.8.9…

Another set 1,3,5,7,9,11,13…

One was extracted from the other …

So you say that there’s:

02040608…

And the new set is only

1,3,5,7,9,11,13…

That’s not true.

The other set is:

1,0,3,0,5,0,7,0,9,0…

Etc…

They are still in 1:1 correspondence!

Does the patter indicate a changing relationship as x goes toward infinity?

Given two infinite sets
A = {1,2,3,4,5,6…}
B = {1,3,5,7,9,11…}

When you take the difference;
C = {0,1,2,3,4,5,…}

We can see that the difference between them is increasing as x goes toward infinity. That would indicate that if that pattern doesn’t change, and I don’t see any reason why it would, one set is reaching toward infinity faster than the other. And even though both are infinite, one is “more infinite”, a greater degree of infinite, than the other.

It would merely be a convention for keeping such things straight. I still don’t think it should be said to be “shorter” or “longer”, merely “lessor” or “greater” in degree or magnitude perhaps.