The discussion revolves around the concept of infinity, specifically whether it can be considered a completed set or if this notion leads to contradictions. Participants explore the philosophical implications of actual versus potential infinities, the mathematical definitions of finite and infinite sets, and the distinctions between discrete and continuous mathematics.
Participants express multiple competing views on the nature of infinity, the distinctions between finite and infinite, and the definitions of mathematical terms. The discussion remains unresolved, with no consensus on the implications of actual infinity or the definitions of related concepts.
Limitations include varying interpretations of mathematical terms such as "data," "measurement," and "precision," as well as differing understandings of discrete versus continuous mathematics. The discussion reflects a mix of philosophical and mathematical perspectives without clear resolutions.
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.pat8126 said: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?
In order to choose one's model of mathematical reasoning to establish a proof, doesn't one need a shared axiomatic understanding of infinity?andrewkirk said: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.
If I understood any of that I would try to answer you.pat8126 said: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?
What is the difference between finite mathematics and continuous mathematics?PeroK said:If I understood any of that I would try to answer you.
Nothing you say concurs with any knowledge I have of mathematics.
You can easily look that up online.pat8126 said:What is the difference between finite mathematics and continuous mathematics?
I already have a concurrence relationship between the information online and my understanding of the question.PeroK said:You can easily look that up online.
What's the question? You've posted this under "general math". Can you phrase your question in mathematical language?pat8126 said: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?
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.PeroK said: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.
pat8126 said: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?
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 said: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.
That's not a maths question.pat8126 said: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?
Math itself deals with patterns and the ability to communicate them to others.PeroK said:That's not a maths question.
A time interval can be modeled 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.
In this sense, mathematics includes a completed infinity.pat8126 said:Math itself deals with patterns and the ability to communicate them to others.
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.pat8126 said: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.
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.pat8126 said: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?