Circular Infinity does not exist

[Davidu]

I was caught up in a "brain storming" today in the literature class.

I tough of 2 types of infinity: linear and circular.

The linear one is truly infinite: nothing repeats, the items go on for ever without repeating...

The circular infinity is like a circle. It is thought that a circle has an infinite number of points. But at least one (actually all the points) repeat. That means that theor number is finite, otherwise it would never have reached any of the points previously marked (or already "visited").

What do you think? Am I right? If not tell me why. Also post you own opinions.

[Acriku]

There are an infinite number of points in a circle. If you start trying to list all the points of a circle - (x)^2 + (y)^2 = 1, e.g. - you will see this.

[Davidu]

I mean if you mark every point of circle you'll reach the first point you have marked (someday).

It's like curved space: you leave Earth, travel for a looooong period of time and then you reach Earth again. That means that space is finite 'cause you got back from where you left.

This kind of space infinity is "relative infinity", that meaning that is infinite in compariosn with our methods of exploring it. But, nevertheless, it is finite.

That is what I think: if reach the point you left earlier that the space you're in is finite.

[Warlord Ripskar]

That's not what circular infinity means.

It means you keep going round without ever reaching the end. There is no edge of the world to fall off, If you kepp moving in one direction you can do so for infinity.

[Davidu]

What you said it's the definition of a parabole. It's a circle that never closes...

I was talking about a cricle. I was trying to prove that the number of points has to be finite.

[Warlord Ripskar]

There are an infinate number of points in any given space, it depends on how fine you want to take it. Try measuring a full stop in micro-quarks.

[Davidu]

Well, is it actually infnite or is it infinite relative to our dimentions?

[Warlord Ripskar]

There is in theory no limit to the detail in which you can measure a point so it is infinate.

[SpiceGuid]

My opinion:

The circle is one object with two operations:

* traversal of the circle-path

* enumeration of the circle-points

* the traversal is time-limited

* the enumeration is infinite

So limited/infinite is a feature of the operation, not a feature of the circle.

The same applies to linear infinity: it appears infinite as both traversal and enumeration, however it is one single object as a whole. You can translate, rotate and scale an infinite line in a constant time. So a line is actually finite regarding translation, rotation and scaling operations. When you say a line is infinite you just consider traversal and enumeration operations. But a line is actually finite if you consider just itself.

[Davidu]

Ok, but what about space?

Is it linear or curved?

[SpiceGuid]

Ok, but what about space?

Is it linear or curved?

You mean outer space?

It is inflating.

Apart that, who knows?

[sneezer3]

Shouldn't this be in the general forum?

[Davidu]

No, this shouldn't be there. The name of this thread in Politics, religion and PHILOSOPHY! We should add science, but the name would become too long.

SpiceGuid: yeah, I meant the outer space. You say it is inflating? It would be interesting to start a voyage and eventually end up in the same spot where you first left. On Earth this was possible 'cause Earth is a sphere and Magellan could sail on it's surface. If the outer space is curved it should be a hollow shpere. We could be inside a huge Easter egg lol.

[SpiceGuid]

Outer space is inflating so by the time you travel the universe is even bigger. May be you can not traverse universe, not even theoritically. May be universe inflates faster than you travel.

In my opinion you can not find the "end" of universe.

End would be boring anyway, isn't it?

[Davidu]

Well, it's nice to know that there's a limit somewhere, so you'll have to explore for it. The fact that is unreachable give it a mistery smell.

:)

[SpiceGuid]

Another possibility: the universe can be both unfinite and expanding. This is no contradiction. In this case expansion just means space dilution, eventually until total void.

[Davidu]

Infinite and expanding means already infinte. You cannot expand the infinte, I mean, can you find any number greater that infinite?

[emprworm]

conceptually, the amount of points between any 2 points is infinite.

however, the number of ACTUAL points between any 2 points is always finite.

when a point is defined as "infinitely small" it is equal to nothing. It does not approximate nothing....it does not approach nothing...infinitely small IS nothing.

So when you talk of points as in "infinitely small" points, you are basically saying "there are an infinite amount of nothings in this circle such that no matter how many nothings you add, you will never get the sum of the circle." This, of course, is correct.

Note:

The mathematical equation that an infinitely small quantity EQUALS zero (not approaches zero, but EQUALS zero) follows:

1 - .9999~(repetend) = 0

[nemafakei]

A point cannot have length, breadth, or depth, else it'd be a line, plane or polyhedron. Why do you assume it cannot have 0 length? It is a point, and has only position, not substance.

If you have two points, A, and B, then there will always conceivably be a midpoint, M, half way between them.

You will then have A, B, M. by the above logic, there is a midpoint of A and M, and a midpoint of A and that, and so on ad infinitum.

[emprworm]

A point cannot have length, breadth, or depth, else it'd be a line, plane or polyhedron. Why do you assume it cannot have 0 length? It is a point, and has only position, not substance.

If you have two points, A, and B, then there will always conceivably be a midpoint, M, half way between them.

You will then have A, B, M. by the above logic, there is a midpoint of A and M, and a midpoint of A and that, and so on ad infinitum.

those points exist conceptually, but not actually. there is no such thing as an actual infinite set in the natural universe. the only way such a set could exist, is if the universe itself is infinite, and most scholars do not think that is the case.

[Davidu]

Seems logic...

I'll have to find some time to "digest" that.

[nemafakei]

"those points exist conceptually, but not actually"

Of course. They are no more real than any line, plane or polyhedron you may care to offer - they are points.

"actual point" - would you care to tell me what you mean by it, and why it's different from a conceptual one?

<|Thankyou for correcting me.|>

[Warlord Ripskar]

"Only two things are truely infinate, the Universe and Human stupidity. But I'm not sure about the Universe."

Albert Einstein

[Davidu]

LOOOL!

Warlord, is that pure philosophy? If it is I like it. ;D

[emprworm]

to say something is actual as in it exists as an objective thing in this natural universe requires measurement. Anything measurable cannot possibly be infinite in scope- either the thing being measured, or to declare an infinite amount of them...unless the universe itself is infinite. But regardless, you cannoth have an infinite amount of actual things that exist (which a point of would if it were actual) in a finite amount of space (any line). The only way around this is to say that a point that actually exists would be infinitely small- which of course would be equal to zero.