Argument Against an Actually Infinite Quantity

[IWantGod]

1. Any actual quantity of something is a distinct quantity - it is an actual number no greater or smaller than the distinct units of which it is comprised.
2. There is no distinct quantity that is greater than a finite number. This is to say that no matter how many units you add together, there is no number that can be reached which can by definition transcend a finite amount. It is always finite
3. An actual infinite cannot be defined as a distinct or particular quantity because there is no quantity greater than a finite quantity. This is to say that if a quantity by definition is made up of finite distinct units it would have to be possible in principle to transcend a finite quantity in order to achieve an infinite quantity. This cannot happen.

Conclusion: Therefore it is meaningless to define an actual infinite as a quantity of distinct finite units.

 

[GEddie]

1. Any actual quantity of something is a distinct quantity - it is an actual number no greater or smaller than the distinct units of which it is comprised.
2. There is no distinct quantity that is greater than a finite number. This is to say that no matter how many units you add together, there is no number that can be reached which can by definition transcend a finite amount. It is always finite
3. An actual infinite cannot be defined as a distinct or particular quantity because there is no quantity greater than a finite quantity. This is to say that if a quantity by definition is made up of finite distinct units it would have to be possible in principle to transcend a finite quantity in order to achieve an infinite quantity. This cannot happen.

Conclusion: Therefore it is meaningless to define an actual infinite as a quantity of distinct finite units.

Well, OK, but who is trying to define infinity in this way?

ICXC NIKA

 

[Nigel7]

If you are crossing the street and can only go half the distance across at a time then you would never get across the street since a distance (or anything) can be divided an infinite number of times. Everything is infinitely divisible.

Doesn’t have so much to do with this thread, I suppose, but it’s cool to think about, and can give some perspective on the concept of infinity which can be difficult to grasp.

https://s6.postimg.org/72qbpdqap/Untitled343444.jpg

Infinity contained in a finite space. Or maybe we only perceive the distance across the street as finite when really that distance and all things are actually infinite.
Hmmm

 

[fisherman_carl]

If infinite means without end then there can not be an infinite past. Since an infinite past would imply that this infinite past ends at the present moment. Where, the past is no longer, and it is the present moment.

 

[Beryllos]

1. Any actual quantity of something is a distinct quantity - it is an actual number no greater or smaller than the distinct units of which it is comprised.
2. There is no distinct quantity that is greater than a finite number. This is to say that no matter how many units you add together, there is no number that can be reached which can by definition transcend a finite amount. It is always finite
3. An actual infinite cannot be defined as a distinct or particular quantity because there is no quantity greater than a finite quantity. This is to say that if a quantity by definition is made up of finite distinct units it would have to be possible in principle to transcend a finite quantity in order to achieve an infinite quantity. This cannot happen.

Conclusion: Therefore it is meaningless to define an actual infinite as a quantity of distinct finite units.

Indeed, some mathematicians prefer not to say that a quantity “goes to infinity,” but rather that it “increases without bound.” For example, the function f(x)=1/x increases without bound as x approaches zero.

 

[GEddie]

In the Wide World of Math, goes to infinity" is simply colloquial for approaches infinity, or represented as

x -----> oo

Where oo is ASCII for the infinity sign.

It is not asserted that the domain or the range in fact includes infinity.

ICXC NIKA

 

[John_Martin]

Infinity is a universal understanding, not an actuality. It is part of “knowing” quantity, the idea of “number”.

And the purpose of understanding infinity is so that when working with actual number you can be confident that any actual number or quantity continues in the range of number, within all the “laws” of mathematics, because you understand the universal “infinity” and because you understand the universal “one” (or “unity”).

The actual quantity or number has not transcended number because number has no bounds and individual numbers are “one”. Universal knowings enable the understanding of individual actualities, as to what they really are, but you cannot find the universal actually.

You may say, “but I can see “one” actually, one tree, etc.”. But you are not seeing “one”, rather seeing several, and your understanding is identifying each individual thing by the idea or universal of “one”, so that you understand you are seeing individual things (“what they really are individually” rather than seeing a big single blob of vision with no distinction of individual things). Actuals are given quantitative meaning by knowing or understanding the universal(s)

 

[fisherman_carl]

If you are crossing the street and can only go half the distance across at a time then you would never get across the street since a distance (or anything) can be divided an infinite number of times. Everything is infinitely divisible.

Doesn’t have so much to do with this thread, I suppose, but it’s cool to think about, and can give some perspective on the concept of infinity which can be difficult to grasp.

https://s6.postimg.org/72qbpdqap/Untitled343444.jpg

Infinity contained in a finite space. Or maybe we only perceive the distance across the street as finite when really that distance and all things are actually infinite.
Hmmm

Your example illustrates the idea that distance can theoretically be divided infinitely. However, in reality your example would not work because in reality humans are not capable of moving the increasingly infinitesimal distances, because humans are finite limited creatures. Thus, if you actually attempted your illustration you would eventually get to the other side. Or you would stop moving altogether. But, as long as you kept moving you would get there.

Parmenides thought that change was impossible. Him and Zeno said that there was infinite distance between any 2 points, and since such a distance is impossible to traverse then it is impossible to move, and our senses telling us we are moving is an illusion. Of course they would be right if there was infinite distance between any 2 points. However, there is not. There is only a potential infinite, not an actual infinite number of points along a line. If we had to traverse an actual infinite number of points then we would never get to our destination.

 

[Neildown]

I would recommend looking up V-Sauce on Youtube - “Counting to Infinity”. While infinity isn’t actually a number, it does give us a concept to work with in theories that deal with numbers. You can also have infinities that contain more or less things than other infinities.

 

[e_c]

I would recommend looking up V-Sauce on Youtube - “Counting to Infinity”. While infinity isn’t actually a number, it does give us a concept to work with in theories that deal with numbers. You can also have infinities that contain more or less things than other infinities.

This is the really weird part about it. When I see those kinds of demonstrations, it gets me wondering if there is something very subtly wrong with them, through some kind of hidden equivocation.

 

[Pat_Albertson]

1. Any actual quantity of something is a distinct quantity - it is an actual number no greater or smaller than the distinct units of which it is comprised.
2. There is no distinct quantity that is greater than a finite number. This is to say that no matter how many units you add together, there is no number that can be reached which can by definition transcend a finite amount. It is always finite
3. An actual infinite cannot be defined as a distinct or particular quantity because there is no quantity greater than a finite quantity. This is to say that if a quantity by definition is made up of finite distinct units it would have to be possible in principle to transcend a finite quantity in order to achieve an infinite quantity. This cannot happen.

Conclusion: Therefore it is meaningless to define an actual infinite as a quantity of distinct finite units.

What is the infinite sum of 1 + 1/2 + 1/4 + 1/8 + . . . and so on forever and ever? Can fractions be both distinct and finite? Why did I start off with the number 1 as opposed to the diagram in post #3 which started off with a semicircle of 1/2 as the diameter? What is this type of series? Have you taken 1st year college calculus (I suppose they offer this in some high schools too though.)?

I’m not trying to be challenging here, just probing what you mean, and where you are mathematically is all.

 

[lmelahn]

What is the infinite sum of 1 + 1/2 + 1/4 + 1/8 + . . . and so on forever and ever? Can fractions be both distinct and finite? Why did I start off with the number 1 as opposed to the diagram in post #3 which started off with a semicircle of 1/2 as the diameter? What is this type of series? Have you taken 1st year college calculus (I suppose they offer this in some high schools too though.)?

I’m not trying to be challenging here, just probing what you mean, and where you are mathematically is all.

This is basically Zeno’s paradox (as is post no. 3).

Although in the idealized world of mathematics, we generally think of numbers as quasi-subsistent entities, in the real world, numbers translate into the property called quantity (continuous quantity, or length, in this case).

For example, in the real world, a two-foot pole is currently (or “actually”) two feet long, no more and no less. It could potentially be cut down into smaller lengths (and—forgetting about quantum indetermination for the moment—could be cut down into arbitrarily short pieces), but at the moment it is two feet long.

So, we are still left with a merely potential infinity of parts, here, it seems to me.

Note that I think an actual infinity in extension is at least theoretically possible. (I.e., it is not repugnant to reason to imagine a body that is immeasurably large in one or more dimensions.) Such a body, however, would not be measurable by units—it would be, in the etymological sense—immense.

 

[lmelahn]

1. Any actual quantity of something is a distinct quantity - it is an actual number no greater or smaller than the distinct units of which it is comprised.
2. There is no distinct quantity that is greater than a finite number. This is to say that no matter how many units you add together, there is no number that can be reached which can by definition transcend a finite amount. It is always finite
3. An actual infinite cannot be defined as a distinct or particular quantity because there is no quantity greater than a finite quantity. This is to say that if a quantity by definition is made up of finite distinct units it would have to be possible in principle to transcend a finite quantity in order to achieve an infinite quantity. This cannot happen.

Conclusion: Therefore it is meaningless to define an actual infinite as a quantity of distinct finite units.

I agree with the conclusion as written, but I don’t think it disproves the possibility of a body that is immeasurably large in one or more of its dimensions. It could, it seems to me, exist; it simply would not be measurable by units.

 

[PseuTonym]

Conclusion: Therefore it is meaningless to define an actual infinite as a quantity of distinct finite units.

The standard practice is to define aleph null (an actual infinite cardinality) as the cardinality of the set of positive integers.

As you are using the word “quantity”, what is supposed to be the difference between quantity and cardinality?

“Quantity” seems to be a more versatile word, allowing us to talk about measure, such as the area of a circle.

It seems that you are attempting to make the word “quantity” do the work of restricting things to just the positive integers, so that there is no “point at infinity.” However, if your “units” are all the same size, then you cannot even talk about half of a unit interval within the realm of “quantity of units.”

Is it meaningless to speak of an actual half as a quantity of distinct finite units?

 

[rossum]

1. Any actual quantity of something is a distinct quantity - it is an actual number no greater or smaller than the distinct units of which it is comprised.
2. There is no distinct quantity that is greater than a finite number. This is to say that no matter how many units you add together, there is no number that can be reached which can by definition transcend a finite amount. It is always finite
3. An actual infinite cannot be defined as a distinct or particular quantity because there is no quantity greater than a finite quantity. This is to say that if a quantity by definition is made up of finite distinct units it would have to be possible in principle to transcend a finite quantity in order to achieve an infinite quantity. This cannot happen.

Conclusion: Therefore it is meaningless to define an actual infinite as a quantity of distinct finite units.

You really need to read Cantor on transfinite numbers if you are going to talk about infinity in any mathematically precise sense. Yes, this does require some reasonably advanced pure mathematics.

If you just want imprecise verbal concepts then you can ignore the mathematics.

rossum

 

[JuanFlorencio]

I would recommend looking up V-Sauce on Youtube - “Counting to Infinity”. While infinity isn’t actually a number, it does give us a concept to work with in theories that deal with numbers. You can also have infinities that contain more or less things than other infinities.

Yes, it gives something to work with. For example, if you start thinking that infinity is a proper mathematical object, you can get to the conclusion, for instance, that the total sum of the natural numbers (which are all positive, and non fractions) is a negative fraction, which is crazy. Obviously, there is something wrong with the first assumption.

 

[JuanFlorencio]

What is the infinite sum of 1 + 1/2 + 1/4 + 1/8 + . . . and so on forever and ever? Can fractions be both distinct and finite? Why did I start off with the number 1 as opposed to the diagram in post #3 which started off with a semicircle of 1/2 as the diameter? What is this type of series? Have you taken 1st year college calculus (I suppose they offer this in some high schools too though.)?

I’m not trying to be challenging here, just probing what you mean, and where you are mathematically is all.

The series tends to 2 as you add elements to it. That is it.

 

[JuanFlorencio]

Note that I think an actual infinity in extension is at least theoretically possible. (I.e., it is not repugnant to reason to imagine a body that is immeasurably large in one or more dimensions.) Such a body, however, would not be measurable by units—it would be, in the etymological sense—immense.

If you can conceive an “actual infinity” (I don’t think you really can), then it is not an infinity.

 

[rossum]

What is the infinite sum of 1 + 1/2 + 1/4 + 1/8 + . . . and so on forever and ever?

Let S = 1 + 1/2 + 1/4 + 1/8 + . . .

Then 2S = 2 + 1 + 1/2 + 1/4 + 1/8 + . . .

So, 2S - S = 2 + (1 - 1) + (1/2 - 1/2) … where all the fractional terms cancel out.

2S - S = 2

S = 2

Your infinite sum totals 2.

rossum

 

[JuanFlorencio]

You really need to read Cantor on transfinite numbers if you are going to talk about infinity in any mathematically precise sense. Yes, this does require some reasonably advanced pure mathematics.

If you just want imprecise verbal concepts then you can ignore the mathematics.

rossum

What is the first mathematical evident proposition that serves as the foundation of the theorem “There is an actual infinity”?