Reply Mon 24 May, 2010 12:03 am
Because I think numbers are actually just rarefied language, a language reduced to quantity, I put this in the language philosophy section.

First we have just plain old numbers, like "3." Now 3 is already an abstraction, because threeness doesn't exists, so far as I can tell, in Nature. We see three cows, or three trees, etc. After having seen enough groups of "three," we learn to abstract "threeness" from these groups.

But then we get to higher abstractions like "x" or "n" which stand not for a first level abstraction like "3," but rather for this class of first level abstractions in general.

We also have classes like "dog" which applies to all particular dogs, in all of their variety. Then we have a higher abstraction like "animal." And above that "life."

Then we can even go so far as to make an abstraction like "abstraction" or "class." Is there a highest level abstraction? What are the complications of this? What do abstractions do for us? In what way, if any, do they exist?
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Native Skeptic
 
  1  
Reply Mon 24 May, 2010 12:18 am
@Reconstructo,
Reconstructo;167979 wrote:
Is there a highest level abstraction?


Infinity.

Only by inclusion of everything could you guarantee no further abstraction.

I think an even better question, is there a highest level of precision? Could one be so specific it would be impossible for any form of abstraction?
Deckard
 
  1  
Reply Mon 24 May, 2010 12:30 am
@Reconstructo,
The levels of abstraction seem to grow ever more objective and ever departing from subjective experience such as the subjective experience of seeing three trees or petting three dogs. If we go in the opposite directino do we get ever more subjective? Descartes? Yet the Cogito or some variation of it seems to has at least the flavor of objective truth. If we turn around again and head towards the ultimate abstraction will we arive at something with the flavor of subjectivity. ("Flavor" is not the best word; please post a better word if you have one.) The abstraction seems to grow ever more inclusive though ever more general. The skeptisim of the subjective path or Descartes version of it seems to grow ever more subtractive until we arive at the one sure thing that tastes like objectivity. Orroborus? The snake tasting its own tail? Can the tail taste it's own head? Maybe it justs poops in the it's own mouth? What? Yuck!
0 Replies
 
ughaibu
 
  1  
Reply Mon 24 May, 2010 12:43 am
@Native Skeptic,
Native Skeptic;167981 wrote:
Infinity.

Only by inclusion of everything could you guarantee no further abstraction.
Infinity doesn't include everything.
Reconstructo
 
  1  
Reply Mon 24 May, 2010 12:44 am
@Native Skeptic,
Native Skeptic;167981 wrote:
Infinity.

Only by inclusion of everything could you guarantee no further abstraction.

I think an even better question, is there a highest level of precision? Could one be so specific it would be impossible for any form of abstraction?


Well, that covers my two favorite questions in this regard. How much can we zoom out? How close can we zoom in? The zoom-in relates I think to the 'ineffable." The zoom out relates to something like "infinity" which is paradoxical. in-finite. Non-finite. If finiteness is boundedness, then finity is a one. So in-finity is something like a negative one. Hegel wrestled with this same problem. He wanted to view the system of human conception as one, but this requires a sort of conceptual moebius strip. It has to contain itself somehow. It's a dynamic "monism"! I like the term "nonism."

---------- Post added 05-24-2010 at 01:49 AM ----------

Deckard;167986 wrote:
The levels of abstraction seem to grow ever more objective and ever departing from subjective experience such as the subjective experience of seeing three trees or petting three dogs. If we go in the opposite directino do we get ever more subjective? Descartes? Yet the Cogito or some variation of it seems to has at least the flavor of objective truth. If we turn around again and head towards the ultimate abstraction will we arive at something with the flavor of subjectivity. ("Flavor" is not the best word; please post a better word if you have one.) The abstraction seems to grow ever more inclusive though ever more general. The skeptisim of the subjective path or Descartes version of it seems to grow ever more subtractive until we arive at the one sure thing that tastes like objectivity. Orroborus? The snake tasting its own tail? Can the tail taste it's own head? Maybe it justs poops in the it's own mouth? What? Yuck!


It's a tricky issue. It seems that most of our language is composed of universals. So to speak is almost always to speak objectively. I think qualia are the height of the subject, perhaps. And then within our semi-objective language/though, we seem to have a hierarchy of abstractions that rise into greater and more inclusive generality, until we have concepts like "universe" or "everything" or "life" or "being." To me, this is an interesting question. Is it the negation of accident that produces essence?

It also seems to me that any term less inclusive than the "all" is dependent upon negation. To have "dog" we must have "non-dog." To have "justice", we must have "in-justice". And maybe this is why the most general concept is paradoxical. It's a donut without a hole. I think negation is crucial to human thinking.
0 Replies
 
Native Skeptic
 
  1  
Reply Mon 24 May, 2010 02:17 am
@ughaibu,
ughaibu;167989 wrote:
Infinity doesn't include everything.


Infinity is, by definition, the sum of everything.

Quote:
Well, that covers my two favorite questions in this regard. How much can we zoom out? How close can we zoom in? The zoom-in relates I think to the 'ineffable." The zoom out relates to something like "infinity" which is paradoxical. in-finite. Non-finite. If finiteness is boundedness, then finity is a one. So in-finity is something like a negative one. Hegel wrestled with this same problem. He wanted to view the system of human conception as one, but this requires a sort of conceptual moebius strip. It has to contain itself somehow. It's a dynamic "monism"! I like the term "nonism."
It would be difficult to say. Ultimately the only way one could define either is with an abstract concept that would be synonymous for it without actually explaining it. Any level of precision or obscurity could be expanded on by simply including or deluding from the previous example, such x-1 or x+1.


Quote:
It's a tricky issue. It seems that most of our language is composed of universals. So to speak is almost always to speak objectively. I think qualia are the height of the subject, perhaps. And then within our semi-objective language/though, we seem to have a hierarchy of abstractions that rise into greater and more inclusive generality, until we have concepts like "universe" or "everything" or "life" or "being." To me, this is an interesting question. Is it the negation of accident that produces essence?

It also seems to me that any term less inclusive than the "all" is dependent upon negation. To have "dog" we must have "non-dog." To have "justice", we must have "in-justice". And maybe this is why the most general concept is paradoxical. It's a donut without a hole. I think negation is crucial to human thinking.
Similar to adaption. In order to examine stimuli there must be a sometimes lack of such stimuli, or else one will adapt to it and the stimuli will no longer exist.






ughaibu
 
  1  
Reply Mon 24 May, 2010 02:21 am
@Native Skeptic,
Native Skeptic;168012 wrote:
Infinity is, by definition, the sum of everything.
You are mistaken, look it up.
TuringEquivalent
 
  1  
Reply Mon 24 May, 2010 02:24 am
@Native Skeptic,
Native Skeptic;168012 wrote:
Infinity is, by definition, the sum of everything.



No, it is not. eg: The set of even numbers is infinite, but they are a proper subset of the natural numbers.

or

{ ...-4, -2, 0, 2 ,4 ..} is a infinite, but a proper subset of { ...-2, -1, 0, 1, 2...}
0 Replies
 
Native Skeptic
 
  1  
Reply Mon 24 May, 2010 02:31 am
@ughaibu,
ughaibu;168014 wrote:
You are mistaken, look it up.


I'm not. One of the definitions of infinity is "endless in measurement of time, space, and quantity."

Anything that would not be included in that would mean something taking up space, time, or quantity outside of infinity, thus making infinity finite. Only something that has a non-quantity could be outside of that, which would be 0, or nonexistent.

---------- Post added 05-24-2010 at 02:35 AM ----------

TuringEquivalent;168015 wrote:
No, it is not. eg: The set of even numbers is infinite, but they are a proper subset of the natural numbers.

or

{ ...-4, -2, 0, 2 ,4 ..} is a infinite, but a proper subset of { ...-2, -1, 0, 1, 2...}


See my above post. I wasn't talking in sequence of numbers, I was speaking in measurements of objects. A sequential infinity is different than an objective infinity.
TuringEquivalent
 
  1  
Reply Mon 24 May, 2010 02:42 am
@Native Skeptic,
Native Skeptic;168016 wrote:
I'm not. One of the definitions of infinity is "endless in measurement of time, space, and quantity."

Anything that would not be included in that would mean something taking up space, time, or quantity outside of infinity, thus making infinity finite. Only something that has a non-quantity could be outside of that, which would be 0, or nonexistent.

---------- Post added 05-24-2010 at 02:35 AM ----------



See my above post. I wasn't talking in sequence of numbers, I was speaking in measurements of objects. A sequential infinity is different than an objective infinity.



That is not true. Any quantities you can construct, and is indeed infinite. I can propose a quantity different from the first quantity that is outside of it.
eg: If you pick an infinite set of circles of infinite many possible radius. I can pick any triangle, and it which would not be part of your set. Thus, you set is infinite, but not everything.
0 Replies
 
ughaibu
 
  1  
Reply Mon 24 May, 2010 02:42 am
@Native Skeptic,
Native Skeptic;168016 wrote:
Anything that would not be included in that would mean something taking up space, time, or quantity outside of infinity, thus making infinity finite. Only something that has a non-quantity could be outside of that, which would be 0, or nonexistent.
Your view is incoherent; if there is a collection of every thing, then that collection is finite and if there is an infinite collection, that collection has lower cardinality than its power set, so it isn't everything, in short, infinity and everything are unrelated notions. Look it up, tell you what, I'll save you the effort, just read: Peter Suber, "Infinite Sets"
TuringEquivalent
 
  1  
Reply Mon 24 May, 2010 02:46 am
@Native Skeptic,
Native Skeptic;168016 wrote:
I'm not. One of the definitions of infinity is "endless in measurement of time, space, and quantity."

Anything that would not be included in that would mean something taking up space, time, or quantity outside of infinity, thus making infinity finite. Only something that has a non-quantity could be outside of that, which would be 0, or nonexistent.

---------- Post added 05-24-2010 at 02:35 AM ----------



See my above post. I wasn't talking in sequence of numbers, I was speaking in measurements of objects. A sequential infinity is different than an objective infinity.


That would not matter at all. Whatever quantities can you possible device in your imagination, and is infinite. i can defined it as a set of mathematical objects isomorphic with your physical quantities so that my argument will hold regardless.
0 Replies
 
Native Skeptic
 
  1  
Reply Mon 24 May, 2010 03:23 am
@ughaibu,
ughaibu;168020 wrote:
Your view is incoherent; if there is a collection of every thing, then that collection is finite and if there is an infinite collection, that collection has lower cardinality than its power set, so it isn't everything, in short, infinity and everything are unrelated notions. Look it up, tell you what, I'll save you the effort, just read: Peter Suber, "Infinite Sets"


Anything given property would be additive to the undefinable infinity in this particular definition. You make an assertion that, including ideas, everything has a finite limit, but with a concept of infinity that it is a false statement as infinity itself is an idea. Furthermore, you don't seem to understand the dynamics of the x+1 x-1 example I gave. A similar numerical could be shown in which infinity is never defined due to even the thought of it itself adds upon itself, thus making it undefinable.

In simple terms, an infinite of things would be everything, as any thing that exists outside of this would break infinite of things since it secludes this thing.


Quote:
That would not matter at all. Whatever quantities can you possible device in your imagination, and is infinite. i can defined it as a set of mathematical objects isomorphic with your physical quantities so that my argument will hold regardless.
This is also incorrect. All ideas and object would be given a property of 1. You can make this whatever you like, it doesn't really matter. X would be the established or existent number of objects/ideas and the +1 would be the addition of the ideology of such a concept, thus adding upon itself, becoming the new x. This pattern would then repeat since the sum of all ideas would have to contain all ideas including itself.

I suppose I was mistaken since even this can be described as sequential, as in an infinity of things would be synonymous with an infinity of even numbers. With an expansive pattern of even numbers, no even numbers will be excluded above the initial even number(If so, tell me which even number and then I can know which thing could exist outside a infinity of things. Very Happy)


It is a difficult concept to grasp, but it's a valid one nonetheless.
TuringEquivalent
 
  1  
Reply Mon 24 May, 2010 04:01 am
@Native Skeptic,
Native Skeptic;168033 wrote:



This is also incorrect. All ideas and object would be given a property of 1. You can make this whatever you like, it doesn't really matter. X would be the established or existent number of objects/ideas and the +1 would be the addition of the ideology of such a concept, thus adding upon itself, becoming the new x. This pattern would then repeat since the sum of all ideas would have to contain all ideas including itself.

I suppose I was mistaken since even this can be described as sequential, as in an infinity of things would be synonymous with an infinity of even numbers. With an expansive pattern of even numbers, no even numbers will be excluded above the initial even number(If so, tell me which even number and then I can know which thing could exist outside a infinity of things. Very Happy)

It is a difficult concept to grasp, but it's a valid one nonetheless.



It is general agreed upon that the idea of an object is different from the object itself. This distinction collapses if idealism is true. So, it is not correct to say ideas and objects share come common property if you are not an idealist.

Suppose as you say; they do share a common property. It does not follow that that property is additive! 2 table is not a table, it is might be something else.

As you point out, you can have infinite number of whatever stuff you want. Label it in a sequence. I can construct a object not in your sequence. Why? How? I define an object as the subset of the original set. So that the power set of your set is larger than your set, but this is impossible since nothing is larger than "everything". It causes problems because you suppose a set that contains "everything" is possible.

it is not possible even in principle.
Native Skeptic
 
  1  
Reply Mon 24 May, 2010 04:27 am
@TuringEquivalent,
TuringEquivalent;168038 wrote:
It is general agreed upon that the idea of an object is different from the object itself.

I agree. This doesn't impede my argument, however, since "thing" could easily be defined to hold both ideas and objects.
Quote:

This distinction collapses if idealism is true. So, it is not correct to say ideas and objects share come common property if you are not an idealist.
That's not true. Both ideas and objects have some quality that distinguish them from nonexistence. No one can make an argument for the nonexistence of ideas, for a lack of idea is also possible, and that would make a non-nonexistence, and a double negative which is silly.

Quote:

Suppose as you say; they do share a common property. It does not follow that that property is additive! 2 table is not a table, it is might be something else.
But we're not talking about infinite tables, were talking about infinite things, abstraction, remember.

Quote:

As you point out, you can have infinite number of whatever stuff you want. Label it in a sequence. I can construct a object not in your sequence. Why? How? I define an object as the subset of the original set. So that the power set of your set is larger than your set, but this is impossible since nothing is larger than infinite.
The thing you're not seeing is that things can infinitely expand but they will have a limitation in their detraction, ultimately, you will reach 1 thing, then no things. So, if infinity is began at the one and expanded, the only thing outside of such would have the property of 0 or nonexistence, as I stated earlier.

Quote:
It causes problems because you suppose a set that contains everything is possible.


I don't suppose. Though I cannot tell you the exact beginning I can know in fact that there is a beginning in set of all objects and ideas, and thus, things, due to the current limitation in subtractive, as eventually I will reach 1, then 0 things, if I could reverse the passage of time.


I apologize for the derailing of your thread over this, Reconstructo. I didn't realize I'd have explain this ideology and I had assumed people would understand what such a concept would imply.
TuringEquivalent
 
  1  
Reply Mon 24 May, 2010 04:55 am
@Native Skeptic,
Native Skeptic;168045 wrote:
I agree. This doesn't impede my argument, however, since "thing" could easily be defined to hold both ideas and objects.

That's not true. Both ideas and objects have some quality that distinguish them from nonexistence. No one can make an argument for the nonexistence of ideas, for a lack of idea is also possible, and that would make a non-nonexistence, and a double negative which is silly.


But we're not talking about infinite tables, were talking about infinite things, abstraction, remember.

The thing you're not seeing is that things can infinitely expand but they will have a limitation in their detraction, ultimately, you will reach 1 thing, then no things. So, if infinity is began at the one and expanded, the only thing outside of such would have the property of 0 or nonexistence, as I stated earlier.


I apologize for the derailing of your thread over this, Reconstructo. I didn't realize I'd have explain this ideology and I had assumed people would understand what such a concept would imply.



How is a thing defined by ideas of an object, and the object itself? It is mistake to use the word "define", since, basic ontological categories do not "define" other categories, since categories in metaphysics are basic. take the example of an electron, and protons. An electron cannot be defined as a proton, or a variant of a proton, since they are different essentially.


It is not true that nonexistence is a property, since it is generally agreed upon by philosophers that existence is not a property. So, it does not make sense to say they lack the property of existence.


Also, what do you mean by everything "expands". It is an absurd idea. You think the list of "everything" expands? If so, then is there a rate of expansion, right? Did i say it is absurd?


So, the list of things expands so that they become one thing? How is that? If the universe contains only jon, and mary. Is jon+ mary a single thing?


Any why do you make 0, and 1 properties? What do 0, and 1 mean?


"I apologize for the derailing of your thread over this, Reconstructo. I didn't realize I'd have explain this ideology and I had assumed people would understand what such a concept would imply."

Perhaps in your head. what you say is so inconsistent.
Native Skeptic
 
  1  
Reply Mon 24 May, 2010 05:29 am
@TuringEquivalent,
TuringEquivalent;168051 wrote:
How is a thing defined by ideas of an object, and the object itself?

Not a single thing, things. An idea is a thing. An object is a thing. An idea of a object is a thing. A object is not made of an idea of itself. I never claimed that.

Quote:

It is mistake to use the word "define", since, basic ontological categories do not "define" other categories, since categories in metaphysics are basic. take the example of an electron, and protons. An electron cannot be defined as a proton, or a variant of a proton, since they are different essentially.
I never made such a claim.



Quote:

It is not true that nonexistence is a property, since it is generally agreed upon by philosophers that existence is not a property.
Alright, but I thought it was also agreed by philosophers that a "because we say so" argument isn't a valid argument.

Quote:
So, it does not make sense to say they lack the property of existence.
It does not make sense because nonexistence is something that can not be conceived, thus ideas must exist.

Quote:

Also, what do you mean by everything "expands".

I already explained this. I really don't feel like repeating it a third time. X+1.

Quote:

It is an absurd idea. You think the list of "everything" expands? If so, then is there a rate of expansion, right? Did i say it is absurd?
The number of things. I explained this. I'm getting tired of the redundancy.
Quote:

So, the list of things expands so that they become one thing? How is that? If the universe contains only jon, and mary. Is jon+ mary a single thing?
They could be considered, depending on the level of obscurity. I could get more precise, and say Jon alone is multiple things, a tongue, 2 legs, 2 arms, all of which combined make Jon, and Jon and Mary make everything.

Quote:

Any why do you make 0, and 1 properties? What do 0, and 1 mean?
0 is nothing. If you have 0 apples, you have no apples, if you have 0 things, you have no things, or nothing. If time was reversed and things came to not be instead of be, you would eventually reach 1 thing, then nothing.

Quote:

"I apologize for the derailing of your thread over this, Reconstructo. I didn't realize I'd have explain this ideology and I had assumed people would understand what such a concept would imply."

Perhaps in your head. what you say is so inconsistent.
No, I've been fairly consistent. My argument hasn't changed, I've simply clarified.
TuringEquivalent
 
  1  
Reply Mon 24 May, 2010 02:23 pm
@Native Skeptic,
Native Skeptic;168057 wrote:
Not a single thing, things. An idea is a thing. An object is a thing. An idea of a object is a thing. A object is not made of an idea of itself. I never claimed that.

I never made such a claim.



Alright, but I thought it was also agreed by philosophers that a "because we say so" argument isn't a valid argument.

It does not make sense because nonexistence is something that can not be conceived, thus ideas must exist.


I already explained this. I really don't feel like repeating it a third time. X+1.

The number of things. I explained this. I'm getting tired of the redundancy.
They could be considered, depending on the level of obscurity. I could get more precise, and say Jon alone is multiple things, a tongue, 2 legs, 2 arms, all of which combined make Jon, and Jon and Mary make everything.

0 is nothing. If you have 0 apples, you have no apples, if you have 0 things, you have no things, or nothing. If time was reversed and things came to not be instead of be, you would eventually reach 1 thing, then nothing.

No, I've been fairly consistent. My argument hasn't changed, I've simply clarified.



You said:
Quote:

"thing" could easily be defined to hold both ideas and objects.


You use the word "define". Under normal usage, if you define A as B, then everything that is true of A is true of B. Is this the case? No. You can kick a socket ball out the way, but you cannot kick an idea out of the field.

It is always good to base certain views on the judgement of a community of scholars learned in the matter, until someone can convince the judgement of the majority are wrong. You disagree?

How can you claim that something is inconceivable, but you have an idea of it? Don` t inconceivable means that you don` t have an idea of it?


You said that the list of everything "expands", but this an a crazy idea. No, this is a stupid, stupid idea. An expansion implies an expansion rate. What the hell is the rate in this context? Is a joke?


What is your justification for "jon and mary" is one thing? Prove it. here is a hint: You have to show it is an individual with properties different from jon, or mary.


Nothing, and something, or you call it 0, or 1 is not a property of anything. Again, existence is not a property.

What you say is completely ridiculous, and laughable. How much philosophy courses have you taken? Judging from the fact that you say " O is nothing", i say you are probable in high school, right?
Native Skeptic
 
  1  
Reply Mon 24 May, 2010 03:02 pm
@TuringEquivalent,
TuringEquivalent;168180 wrote:
You said:


You use the word "define". Under normal usage, if you define A as B, then everything that is true of A is true of B. Is this the case? No. You can kick a socket ball out the way, but you cannot kick an idea out of the field.


Both a dog and a fish can be called an animal, are they both fully capable of the same things and contain the same properties? No, they're not. Animal is just a more abstract term, just as "thing" is a more abstract term. Animals share a property that makes them animals, just as objects and ideas do, which I explained, and it is not the ability to kick.

All Humans are mammals.
Not all mammals are Humans.
True or false?
If so, are humans and mammals the exact same thing? If so, how can some Mammals be Humans but not others? Really ponder this.

Quote:

It is always good to base certain views on the judgement of a community of scholars learned in the matter, until someone can convince the judgement of the majority are wrong. You disagree?
I disagree that any debate should come to be with the predisposition to any one argument based on any false concept, even ad populum.
Quote:

How can you claim that something is inconceivable, but you have an idea of it? Don` t inconceivable means that you don` t have an idea of it?
Not necessarily. Having an idea of something without a conception of it is very well possible if the lack of such a thing would be impossible. If there are currently finite things, with a unlimited potential for things, then if one managed to take away things from existence one at a time and eventually eliminate everything since the limitation is 0. However, I can infinitely expand(which I've shown how to do plenty of times in this thread) because there's no limitation to how much can come to be. Infinity would then be the potential of things, and it could not represented any other way. Thus, infinity is the sum of all things.

Quote:

You said that the list of everything "expands", but this an a crazy idea. No, this is a stupid, stupid idea. An expansion implies an expansion rate. What the hell is the rate in this context? Is a joke?
The expansion rate is equal the amount of new things coming to be. I can't explain it beyond that but it simply must be, since with even this I am creating new ideas.

Quote:

What is your justification for "jon and mary" is one thing?
What is your justification for "Tongue, Legs, Arms, Heart etc.." as one thing? Are you saying a tongue is not a thing? Are you saying a heart is not a thing? Are you saying Jon would be Jon if he didn't have these things? If a single thing can only be one thing then Jon cannot be a thing since he is made of multiple things and I just showed you how.
Quote:
Prove it.
You prove Jon is one thing. I just listed 4 distinct things that make up Jon.

Quote:
here is a hint: You have to show it is an individual with properties different from jon, or mary.
Actually the thing you're not understanding is a dog is not different than an animal. A dog has the properties of an animal, it's simply more specific. So, if I looked at Jon and Mary and say a similarity, say, they're the only existence, then I can say they are Existence, one thing.

Quote:

Nothing, and something, or you call it 0, or 1 is not a property of anything. Again, existence is not a property.
If I have 0 apples I have no apples. I'm getting tired of explaining my arguments while yours are supposed to just be believed.

Quote:

What you say is completely ridiculous, and laughable. How much philosophy courses have you taken? Judging from the fact that you say " O is nothing", i say you are probable in high school, right?
No, I haven't been in high school for about 5 years now, though I question what my standing has to do with the argument, since if anyone spoke them, they would not change. Why would it matter if I was in High School? You still haven't combated them, you simply said they are "wrong" "stupid" and "laughable". Perhaps you would like to explain to me "why"?
Reconstructo
 
  1  
Reply Tue 25 May, 2010 12:03 am
@Native Skeptic,
Native Skeptic;168016 wrote:
I'm not. One of the definitions of infinity is "endless in measurement of time, space, and quantity."

Anything that would not be included in that would mean something taking up space, time, or quantity outside of infinity, thus making infinity finite. Only something that has a non-quantity could be outside of that, which would be 0, or nonexistent.

---------- Post added 05-24-2010 at 02:35 AM ----------



See my above post. I wasn't talking in sequence of numbers, I was speaking in measurements of objects. A sequential infinity is different than an objective infinity.

I think you are both just using "infinity" in different ways. Smile
0 Replies
 
 

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