Question on actual infinity

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coolduude

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I recently defended the position that an actual infinite cannot be created by succesive addition (add one, add one, add one, etc). I was thinking and stumbled on this problem, which probably has an easy solution. I just can’t figure it out though :o

If one adds, say a billion, to infinity, won’t that create an actual infinite? In other words, if one adds finite quantities forever, won’t that create an actual infinite?

I’m sure there’s an easy solution to this, but it’s just not clicking for me.

Thanks,
coolduude:cool:
 
coolduude said:
I recently defended the position that an actual infinite cannot be created by succesive addition (add one, add one, add one, etc). I was thinking and stumbled on this problem, which probably has an easy solution. I just can’t figure it out though :o

If one adds, say a billion, to infinity, won’t that create an actual infinite? In other words, if one adds finite quantities forever, won’t that create an actual infinite?

I’m sure there’s an easy solution to this, but it’s just not clicking for me.

Thanks,
coolduude:cool:
Click to expand...
I think when you ask the question of adding finite events forever, you are talking about a potential infinite (like the future being infinite etc.). A potential infinite is possible though an actual infinite is not.

God Bless 🙂
 
ddarko said:
I think when you ask the question of adding finite events forever, you are talking about a potential infinite (like the future being infinite etc.). A potential infinite is possible though an actual infinite is not.

God Bless 🙂
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I don’t quite understand how that answers the question. I’m not the best at philosophy :o
 
1+1+1 or Billion+billion+billion will never lead to infinity. (or an actual infinite)

However, if one does a Billion+billion+billion… Forever, it will lead to a potential infinite - because it will continue growing forever; there is no finite limit on it’s potential - even though the figure will never actually be infinite.

Just like if I got 10 and divded by 2… I could theoretically divide it by two for an infinite ammount of time; but no matter how many times I divide it; it won’t have been divided infinite times.

👍
 
Infinity is “infinity” and that is why it is infinity. Whether Actual, definite, completed, existential, absolute, plus or minus, it is still infinity.

If you add one billion to infinity, it is just like adding a drop of water to the ocean. It makes makes no difference. infinity + a billion = infinity. Infinity - a billion = infinity. billion x infinity = infinity , etc., If you divide one by infinity 1/∞, it is just like dividing one into infinite pieces. some mathematicians will say the answer is zero but what happens to the “1” ? If you divide infinity by 1 the answer is infinity.

Infinity is just infinity if it is defined! if it is undefined then you cannot call it infinity.
 
We can add numbers to create an actual universe, but once that actual is achieved, potential infinity continues.

Meaning: We can think of an actual infinite by thinking of our universe. Add up ALL the space (i was going to say all atoms but i am pretty sure there is a set number in the universe? :p), and we can achieve actual infinity. Potential infinity steps in then. What do we get when we take away our actual infinity (universe)… we get “nothing.” And from “nothing” there are potentially infinite number of possibilities that could happen.
 
lemondiesel said:
We can add numbers to create an actual universe, but once that actual is achieved, potential infinity continues.

Meaning: We can think of an actual infinite by thinking of our universe. Add up ALL the space (i was going to say all atoms but i am pretty sure there is a set number in the universe? :p), and we can achieve actual infinity. Potential infinity steps in then. What do we get when we take away our actual infinity (universe)… we get “nothing.” And from “nothing” there are potentially infinite number of possibilities that could happen.
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I don’t think what you say is correct.

An actual infinite doesn’t exist. Only potential infinite can. To make this more clearer, past events of the universe cannot be infinite since this will mean its an actual infinite. The future events of the universe can be infinite since its a potential infinite.
coolduude said:
I don’t quite understand how that answers the question. I’m not the best at philosophy :o
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When you asked the question, your idea of adding things ‘‘forever’’ to get an infinity implies keep adding in the future. The infinite can not be achieved since ‘‘forever’’ cannot at any moment happen. So you are referencing a potential infinite and therefore there is no problem. Hope that clarifies.

God Bless 🙂
 
coolduude said:
If one adds, say a billion, to infinity, won’t that create an actual infinite? In other words, if one adds finite quantities forever, won’t that create an actual infinite?
Click to expand...
Sorry for not getting back to you.

The answer is this. Quantities are definable. That which cannot be defined as a quantity is not really a quantity. If you could count to an infinity, it would not be an infinity. An infinity is not one number away from a finite set. An actual infinity is not a definite number. You cannot define it by a number. Do you know what an infinite number is. No you don’t. You know why? Because you would have to transcend all logically possible quantities of finite numbers in order to define it; and in doing so an infinite would cease to be a number. Why? You cannot complete finite numbers. There is not a highest number which becomes infinity. There is no logically possible quantity that can’t be added to. You can always add one more, and if you can add one more then it has finite quantity of additions. If a quantity has no beginning, then it has transcended all countable quantity; and thus it has ceased to be something that can be defined by a number. Like i said, you cannot complete numbers that exist by addition.

An actual infinite number is an incoherent concept.

I hope that helped. But it probably will lead to more confusion.😉
 
MindOverMatter2 said:
Sorry for not getting back to you.

The answer is this. Quantities are definable. That which cannot be defined as a quantity is not really a quantity. If you could count to an infinity, it would not be an infinity. An infinity is not one number away from a finite set. An actual infinity is not a definite number. You cannot define it by a number. Do you know what an infinite number is. No you don’t. You know why? Because you would have to transcend all logically possible quantities of finite numbers in order to define it; and in doing so an infinite would cease to be a number. Why? You cannot complete finite numbers. There is not a highest number which becomes infinity. There is no logically possible quantity that can’t be added to. You can always add one more, and if you can add one more then it has finite quantity of additions. If a quantity has no beginning, then it has transcended all countable quantity; and thus it has ceased to be something that can be defined by a number. Like i said, you cannot complete numbers that exist by addition.

An actual infinite number is an incoherent concept.

I hope that helped. But it probably will lead to more confusion.😉
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Perhaps I can simplify what you have written.

Infinity is, by definition, unachievable. You can’t count to infinity because you can always continue counting.

An actual infinite would be an achieved infinity. This is impossible since it would entail the existence of an “achieved unachievable” which is a contradiction.
 
ddarko said:
I don’t think what you say is correct.

An actual infinite doesn’t exist. Only potential infinite can. To make this more clearer, past events of the universe cannot be infinite since this will mean its an actual infinite. The future events of the universe can be infinite since its a potential infinite.
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Actual infinity is bound on the physical world. Potential infinity is not.
 
lemondiesel said:
Actual infinity is bound on the physical world. Potential infinity is not.
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No. Actual infinite can’t exist physically. I do not know what you mean by it being bounded by the physical world. It would be a logically contradictory statement to say an actual infinite exists.

Potential infinite can exist because it hasn’t been realized yet. As I said before, the past is actual and therefore cannot be infinite. But the future can be infinite since it will never arrive.

God Bless 🙂
 
Yes, infinity multiplied by a finite number will be infinite. You say, a 1+1 forever… well that’s not a very clear mathematical way of stating the problem. You are basically saying “a number you get from adding 1 infinitely”

1 x infinity = infinity
 
ddarko said:
No. Actual infinite can’t exist physically. I do not know what you mean by it being bounded by the physical world. It would be a logically contradictory statement to say an actual infinite exists.

Potential infinite can exist because it hasn’t been realized yet. As I said before, the past is actual and therefore cannot be infinite. But the future can be infinite since it will never arrive.

God Bless 🙂
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Actual infinite is needs something that can actually be infinite. You can’t have negative something because then it is not actual. Potential infinite is actual infinite but it contains the infinite number of possibilities. Negative and positive infinite exist here. There is a difference between the two, and no its not logically contradictory.

I am taking it you do not believe in an infinite universe? If its infinite, we can realize it. Stars explode and created new ones, maybe new life, continuously forever. Time is actual and potential. The past is the way we got here, an actual infinite following potential. Potential is the present and the future, because like you said, it hasn’t happened yet. Infinite number of things that could happen.

Picture this. When you are about to speak, you think and there is potential infinite for what you could say. When you say it, you have created the actual infinite because you could continue speaking forever (hypothetically).
 
Hubriss said:
Yes, infinity multiplied by a finite number will be infinite. You say, a 1+1 forever… well that’s not a very clear mathematical way of stating the problem. You are basically saying “a number you get from adding 1 infinitely”

1 x infinity = infinity
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Well I was talking about succesive addition to form an actual infinite, but this is cool
too. Infinity is an interesting topic isn’t it?

What’s infinity x 2?
 
coolduude said:
What’s infinity x 2?
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thats just it. infinity with plus, minus, multiple or dividing a number are the potential because if you try to take infinity times something you are assigning a set to what infinity actually equals. Infinite contains all numbers, including the answer the infinity x 2.
 
Which infinity are you discussing. For there are an infinite amount of infinites, and some infinites are larger than others. Quick example will utilize two groups of numbers, Group A. and Group B.
A: 1,2,3,4,5,etc…
B: 2,4,6,8,10etc…
These two number lines can continue for eternity, or what we could define as infinity. But group B will always be larger than group A. Even though they will run side by side in either direction. Thus line B, is a larger infinity.
I see some on here believe that adding a number to a large set of numbers only adds that number to that number. Such as 10+1=11, 11+1=12 etc… But the point of infinity is that this progression would never end, so the act of adding these numbers would be infinite. For you could keep pulling numbers from an infinite amount of numbers. However, do not take my word for it. If you are interested you should study some philosophy of mathematics. Also God is infinite, because he works outside of time, thus if God is infinite than I would believe infinity exist.
 
uscav_21 said:
Which infinity are you discussing. For there are an infinite amount of infinites, and some infinites are larger than others. Quick example will utilize two groups of numbers, Group A. and Group B.
A: 1,2,3,4,5,etc…
B: 2,4,6,8,10etc…
These two number lines can continue for eternity, or what we could define as infinity. But group B will always be larger than group A. Even though they will run side by side in either direction. Thus line B, is a larger infinity.
Click to expand...
That’s not how infinities work.

No matter how many times a number is added, multiplied, divided etc. it will never reach infinity. Even if your 2,4,6… etc. was continued eternally it would never reach an infinite number.

We call this a potential infinite; because it is not boundaried by a finite sum. However, this will never be an actual infinite; because despite it’s growth it will always be a finite number.

👍
 
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