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"Finite but unbounded"

Badly Shaved Monkey

Anti-homeopathy illuminati member
Badly Shaved Monkey
Joined
Feb 5, 2004
Messages
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I just read a passage in a book contrasting something that is infinite with something that is finite but unbounded.

I submit myself to the hilarity of my peers: isn't unbounded the same as infinite, so "finite but unbounded" is an oxymoron?

Thanks.
 
Think of the perimeter of a circle. This is a one-dimensional "space" which has no bounds but is definitely finite. The surface of a sphere is a similar situation with a two-dimensional space.

Add one more dimension and you have what could be a model for our Universe.

Fred
 
Badly Shaved Monkey said:
I just read a passage in a book contrasting something that is infinite with something that is finite but unbounded.

I submit myself to the hilarity of my peers: isn't unbounded the same as infinite, so "finite but unbounded" is an oxymoron?

Thanks.
Click to expand...

Well a sphere is unbounded yet finite in a sense, depending on the given qualification, as it has no bounded break-points to its surface.
 
Badly Shaved Monkey said:
I just read a passage in a book contrasting something that is infinite with something that is finite but unbounded.

I submit myself to the hilarity of my peers: isn't unbounded the same as infinite, so "finite but unbounded" is an oxymoron?

Thanks.
Click to expand...
I predict mention of ants on spheres and questions like “What’s North of North?”.

ETA - Two posts mentoned spheres as I posted. Now all we needs is the ants.
 
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I'm sure someone will be along shortly to explain it better than me but, in the meantime, you can think of it as being like the surface of the globe.

You can travel east for as long as you like with meeting an "edge", yet the surface of the earth is clearly finite. Hence finite yet unbounded. The crucial difference between this and truly infinite is that, in the finite case if you travel far enough, you will eventually get back to where you started.

ETA. Many people turned up before I even finished typing. I am clearly not secretary material.
 
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Being bounded to the surface of a sphere, globe or any shape isn't being unbounded.
 
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What if there were two mobius strips circling each other like the rings in Superman 2 and there was a quantum-tunneling nanobot ant zooming back and forth between them at near c?

Would it be bounded but awesome!
 
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Badly Shaved Monkey said:
I just read a passage in a book contrasting something that is infinite with something that is finite but unbounded.

I submit myself to the hilarity of my peers: isn't unbounded the same as infinite, so "finite but unbounded" is an oxymoron?

Thanks.
Click to expand...
"unounded" is a bad choice of words here, because "bounded" usually means "small enough to fit inside a ball of finite radius". The author probably meant "without boundary".
 
Fredrik said:
"unounded" is a bad choice of words here, because "bounded" usually means "small enough to fit inside a ball of finite radius". The author probably meant "without boundary".
Click to expand...
'Finite but unbounded' is a popular usage meaning 'finite but without boundary'.

For contemporary usage, Google 'finite but unbounded'.
 
ynot said:
Any shape would if "unbounded" means infinite travel around a finite surface. A cube would do.
Click to expand...

It is my understanding that this is correct. Any 3 dimensional shape has a finite but unbounded 2 dimensional surface. If you take away any point from that surface you will have a bounded 2 dimensional surface, but there will still be an infinite number of finite and unbounded lines on that surface.

But I only recently started reading about this myself, so if I am wrong here please correct me.
 
Are fractal figures finite but unbounded?

The Mandelbrot set has a finite area but infinite perimeter
 
Badly Shaved Monkey said:
Thanks, all, for the replies.
Click to expand...

Suppose you had a lever that gave you a dollar every time you pulled it, with no limits to how many dollars you could get. You now have access to a finite but unbounded number of dollars. You will never run out of dollars, but you'll never have an infinite amount of them either unless you pull the lever for an infinite time.

I think that's more or less how someone explained it to me.
 
Kevin_Lowe said:
Suppose you had a lever that gave you a dollar every time you pulled it, with no limits to how many dollars you could get. You now have access to a finite but unbounded number of dollars. You will never run out of dollars, but you'll never have an infinite amount of them either unless you pull the lever for an infinite time.

I think that's more or less how someone explained it to me.
Click to expand...

I probably am not qualified to comment, but that doesn't seem the same as the solid-surface example. Here you assert that the dollars themselves are infinite, but you can only have a finite, but unspecified number of them. Your example is like a journey into infnite space. Space can be infinite, but the number of kilometres you can travel is finite. I don't think that's unbounded, but 'unspecified' or 'yet to be determined'.

"It", the number of dollars you can have or km you can travel, is bounded by your finite life.
 
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Acleron said:
Are fractal figures finite but unbounded?

The Mandelbrot set has a finite area but infinite perimeter
Click to expand...

I didn't know it had a finite area.

Now I'm struggling to remember, but I was reading about examples of infinities where the incremental slope of a line on a graph perpetually declines, but the line is not asymptotic to a finite y-value. That hurt my head. I think Zeno's paradox is so familiar that, ironically, it has become "common sense" and to find something with a similar set-up but a different result is counter-intuitive.
 
Badly Shaved Monkey said:
I didn't know it had a finite area.

Now I'm struggling to remember, but I was reading about examples of infinities where the incremental slope of a line on a graph perpetually declines, but the line is not asymptotic to a finite y-value. That hurt my head. I think Zeno's paradox is so familiar that, ironically, it has become "common sense" and to find something with a similar set-up but a different result is counter-intuitive.
Click to expand...

Damn I was relying on memory and always forget it is unreliable.

I knew a fractal had the infinite boundary and finite area but cannot find out about the Mandelbrot.

So for your delectation I unveil -

The Koch Snowflake
 
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