# Completed infinity

• I

## Summary:

How can infinity ever complete, by definition?

## Main Question or Discussion Point

If actual infinity represents a completed set of infinite data points, wouldn't that be a contradiction of terms?

## Answers and Replies

andrewkirk
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The notion of 'actual infinities' and 'potential infinities' is a philosophical notion that was invented by Aristotle, and later picked up by Aquinas. It is not science or mathematics, but metaphysics, a topic that physicforums does not cover (for good reason, but it would take too long to explain why).

If you type 'philosophy forums' into your favourite internet search engine, you will find a number of places where you would find people willing to discuss this topic.

PeroK
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Summary: How can infinity ever complete, by definition?

If actual infinity represents a completed set of infinite data points, wouldn't that be a contradiction of terms?
Infinite means "not finite". The set of natural numbers ##0, 1, 2 \dots## is not finite. You can always add ##1## to get another number. By definition therefore this is an infinite set.

Klystron
The notion of 'actual infinities' and 'potential infinities' is a philosophical notion that was invented by Aristotle, and later picked up by Aquinas. It is not science or mathematics, but metaphysics, a topic that physicforums does not cover (for good reason, but it would take too long to explain why).

If you type 'philosophy forums' into your favourite internet search engine, you will find a number of places where you would find people willing to discuss this topic.
In order to choose one's model of mathematical reasoning to establish a proof, doesn't one need a shared axiomatic understanding of infinity?

For instance, data measurement within a discrete mathematical model can be defined to a finite level of precision, whilst data measurement within a continuous mathematical model cannot.

Isn't that the difference between using Calculus and finite math to model and solve a problem?

PeroK
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In order to choose one's model of mathematical reasoning to establish a proof, doesn't one need a shared axiomatic understanding of infinity?

For instance, data measurement within a discrete mathematical model can be defined to a finite level of precision, whilst data measurement within a continuous mathematical model cannot.

Isn't that the difference between using Calculus and finite math to model and solve a problem?
If I understood any of that I would try to answer you.

Nothing you say concurs with any knowledge I have of mathematics.

If I understood any of that I would try to answer you.

Nothing you say concurs with any knowledge I have of mathematics.
What is the difference between finite mathematics and continuous mathematics?

PeroK
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What is the difference between finite mathematics and continuous mathematics?
You can easily look that up online.

You can easily look that up online.
I already have a concurrence relationship between the information online and my understanding of the question.

At the moment, the only thing indefinite about your response is your understanding relative to my own.

Are we talking about the same stuff or is there a fundamental misunderstanding that can only be discovered through conversation?

PeroK
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I already have a concurrence relationship between the information online and my understanding of the question.

At the moment, the only thing indefinite about your response is your understanding relative to my own.

Are we talking about the same stuff or is there a fundamental misunderstanding that can only be discovered through conversation?
What's the question? You've posted this under "general math". Can you phrase your question in mathematical language?

Note that, for example, "data", "measurement" and "precision" are not generally mathematical terms.

Also note that "finite" and "discrete" are not the same.

What's the question? You've posted this under "general math". Can you phrase your question in mathematical language?

Note that, for example, "data", "measurement" and "precision" are not generally mathematical terms.

Also note that "finite" and "discrete" are not the same.
If a person needed to measure the number of people on the forum at any given time, it would be a discrete value since there is a finite set of people at any given time.

Do you agree with this proposition?

PeroK
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If a person needed to measure the number of people on the forum at any given time, it would be a discrete value since there are a finite set of people at any given time.

Do you agree with this proposition?
I think we can safely assume that PF has and always will have a finite set of users, online or otherwise.

That's hardly a question worth asking.

I think we can safely assume that PF has and always will have a finite set of users, online or otherwise.

That's hardly a question worth asking.
If one wanted to measure the total number of possible time intervals one could use to sample the size of the physics users on the forums, would that be a finite value or an infinite value?

PeroK
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If one wanted to measure the total number of possible time intervals one could use to sample the size of the physics users on the forums, would that be a finite value or an infinite value?
That's not a maths question.

A time interval can be modelled as a real number. But, in practical terms any measurement can only have a finite set of answers. That's an experimental question.

Maths itself does not deal with "measurements", as I said above. Maths deals with numbers.

That's not a maths question.

A time interval can be modelled as a real number. But, in practical terms any measurement can only have a finite set of answers. That's an experimental question.

Maths itself does not deal with "measurements", as I said above. Maths deals with numbers.
Math itself deals with patterns and the ability to communicate them to others.

jbriggs444
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Math itself deals with patterns and the ability to communicate them to others.
In this sense, mathematics includes a completed infinity.

The Peano axioms are a characterization of a completed infinity -- the natural numbers. They are a "pattern" which can be communicated.

No, this does not involve a contradiction. If you see a contradiction, perhaps you can exhibit it.

PeroK
Mark44
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If a person needed to measure the number of people on the forum at any given time, it would be a discrete value since there is a finite set of people at any given time.
You don't "measure" the number of people in a forum -- you count them. The set of possible values for the number of people in a forum is both discrete (since the count will always be an integral value) and finite. As already mentioned, these are separate concepts.
The postitive integers {1, 2, 3 ...} is a discrete set, since they are separated, but it is also infinite.

Mark44
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If one wanted to measure the total number of possible time intervals one could use to sample the size of the physics users on the forums, would that be a finite value or an infinite value?
Again, we don't "measure" the total number of whatevers -- we count them. The time intervals could be any real, nonnegative length, so there would be an infinite number of them, assuming we could measure time to any desired degree of precision. However, the clock we use is necessarily of the real world, so there are limits to the degree of precision with which we can measure the elapse of time.

And what size are you talking about -- their heights, weights, what? If you mean how many forum users, we don't call that the "size" -- instead, that would be the number or count of users.

You appear to be mixing up two orthogonal concepts -- discrete and infinite. The integers are an infinite set, but are discrete, with any two adjacent integers being separated by one unit. For any integer, there is another integer that is next to it, in either direction. The real numbers are continuous and are also an infinite set. For any real number, thought, there is no "next" real number.

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Mark44
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This thread seems to have run its course, so I am closing it.