Is 1 = 0.999... ? Really?

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.

Like I haven’t pointed out the flaw numerous times before.

The flaw is in #3–your assumption that adding an apple to an infinite set of apples makes the set larger. (And BTW, adding the red apple but removing another apple doesn’t contradict #2, it just means something was left out.)

I’ll go deeper:

Let’s say with infinite sets, the size of the set is undefined, then you can’t increase the size by adding one because, well, how do you increase undefined?

If you don’t like that, then let’s say the size of the set is infinite. Then:

(\infty) + 1 = (\infty)

The size doesn’t change.

Want me to go deeper?

You know what? No! No more deeper for you. You need to be convincing me that what applies to finite sets applies to infinite sets. Let it be known that I agree with your logic in regards to finite sets. So let’s not keep beating that dead horse. Focus your energies on proving that what applies to finite sets also applies to infinite sets.

^ See what I did there? Burden of proof thing. That’s right, bitch. :smiley:

Did you really just ignore this whole post ???

Besides, how do you “reach infinity faster”?!

viewtopic.php?p=2755866#p2755866

Gib,

Magnus already addressed that counter argument with:

To say that you “ADD” something is to say that you made it larger, longer, taller, or whatever fits.

What you are saying is that you cannot add to an infinite set.

Couple things:

  1. When we talk about a set being infinite, we mean it has an infinite number of members, not that the value of each member is closer or further from infinity. So we don’t say the size of set {1, 2, 3} is less than the size of set {2, 4, 6}. They’re both 3 members in size.

  2. The rate at which members of a set approach infinity is different from the size of the set. You can say the rate with which set B approaches infinity is greater than the rate with which set A approaches infinity, but that doesn’t mean set B has more members than A.

My argument addressed this better Than gibs approach, yet you ignore it:

The “highest” order of infinity is:

1.) rational number
2.) uncounted infinity
3.) different rational number
4.) different uncounted infinity

Using this argument, we can determine that if you split it, you’re left with:

1.) rational number
2.) 0
3.) rational number
4.) 0

Etc…

1.) 0
2.) uncounted infinity
3.) 0
4.) uncounted infinity

Etc…

No matter how you divide from the “highest order” the sets will all be in 1:1 correspondence.

Done.

Proof.

QED.

You guys lost.

Now continue your meaningless discussions.

Well okay but just take any one value of the sets as a count for a new set. The new set for B will always be longer than the new set for A. So as x goes to infinity, the new set for B will be infinitely larger in count or longer in “length” than the new set for A, even though they are both infinite.

The pattern of always being longer never changes.

You’re still ignoring me.

Do you want the answer to this or not ?

viewtopic.php?p=2755884&sid=dfdee997b272ae54ab79e6c6362c2cb0#p2755884

I ignore it because I can’t make any sense out of it.

The sense of it is that you can do concept replacements of numbers, and order the concepts in a list.

I’m not listing an actual number here, I’m using that abstract representation of the number with words, to place 1:1 correspondence for the “highest order of infinity”

I call it my cheat.

If mathematicians balk at my abstractions, they can only look at how others balk at theirs.

This is fair game what my proof is.

You haven’t.

If you stop pretending that you did, you will stop being frustrated (which means you will stop posting funny gifs that do nothing but reduce the quality of the discussion.)

I know that frustration is a fashionable thing but that does not mean it’s a positive thing.

It does because premise #2 also states that the line didn’t change in any other way (which means that no green apple was removed from it.)

First of all, the size of infinite sets is not undefined.

To say that a size is undefined is to say that it’s unspecified i.e. that it’s unknown.

But to say that a set is infinite is to say that the number of its elements is greater than every finite number. By definition, every infinite set is larger than every finite set. So it’s not like we know absolutely nothing about the size of infinite sets.

But even if the number of things is undefined (i.e. unknown), by adding one to it you necessarily increase it.

Any number + 1 < Result

That’s what the word “add” means.

That’s not an argument.