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0 pointsjerf15y ago0 comments

You can define any dimensional number that you like, including infinite. What you can't do is get certain properties out of them. But infinite dimensional numbers are actually frequently used, under the term "n-dimensional vector".

(Infinite is often confused for "really big", but a better way of understanding it is often to use the term "unbounded". When we deal with n-dimensional vectors, we're not saying that we are always literally dealing with vectors with a millionybillionytertrillion dimensions, such that we can't even represent one in a real computer, we're saying that there isn't a firm upper limit on the number of dimensions we may encounter. It is often more the "unbounded" aspect of infinity that we are concerned with, rather than the "larger than anything else" aspect.)

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Produce15y ago· 2 in thread

From what I gather from jpallen's response to my other message the properties you're talking about are things like being able to add, multiply, subtract and divide, right? What's to stop one from coming up with novel properties which are unique to these systems? Is our commonly used system basically an arbitrary set of conditions? Do you think that some systems correlate better to how nature does things than others, and if so, which ones would they be?

Ah, so it's unbounded like how Haskell's lazy evaluation treats infinity.

derleth14y ago

> What's to stop one from coming up with novel properties which are unique to these systems?

Interestingness. Usefulness, perhaps, if you have a specific definition of 'useful' in mind.

> Is our commonly used system basically an arbitrary set of conditions?

It's an arbitrary set of conditions with interesting properties, and it's not always obvious which arbitrary conditions will have interesting properties.

> Do you think that some systems correlate better to how nature does things than others, and if so, which ones would they be?

Well, that is an interesting question, which means anyone who claims to know an absolute answer to it is a moron. We do know, for example, that vectors are a very useful tool to model a lot of what happens in physics, and that complex numbers are a compact way to talk about rotation, especially complex exponentiation (taking a real number, such as e, to complex powers).

> Ah, so it's unbounded like how Haskell's lazy evaluation treats infinity.

Yes. For example, a definition (the Peano axioms) of the set of the natural numbers (either the positive or non-negative integers; the set may or may not include zero, as conventions vary) states that the set contains 0 (or 1) and that for every number x it contains, it also contains x+1.

Produce14y ago

I wish they taught this back in school, math would have been so much more interesting. Anyway, I lack the knowledge to ask any more meaningful questions so I'm gonna go do some digging. Thanks for taking the time to respond.

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