size(s) of infinity

[DrPizza]

Inspired by the never ending .9999.... = 1 thread (they ARE equal, but post your comments to that in the other thread)

There are an infinite number of points on a line....
There's an infinite number of points in a line segment (half way between any two points, there's another point)

So, my question to mess up the minds of the people who rely on intuition too much is this:

Are there more points on a two inch line segment than there are on a one inch line segment??

The answer is.....
the answer is removed until you all bicker over it (and I know there will be two sides to this one)

 

[Corporate Thug]

why didnt you let us answer the question

 

[illusion88]

Originally posted by: shady06
why didnt you let us answer the question

yeah

why?

 

[MichaelD]

There are no points because there really is no line.

I = Teh Winnar.

 

[Nebor]

I doubt there will be two sides. If in any given line there are infinite points, then the length of the line is irrelevant. There are infinite points in a 1 inch line, and infinite points in a 2 inch line.

 

[TuxDave]

If I had to guess, I would say that there are more points in a two inch segment than in a one inch segment. I'm thinking this:

If we divide the two inch segment into 2 one inch segments and line it all side by side. We see that for every point in the one inch segment, we can directly map two points, one in each of the 2 one inch segments. So since we will always have that ratio of 1:2, the two inch segment will contain more points?

 

[KEV1N]

Wouldn't the number of points on both segments have cardinality "R" (equivalent to the real numbers)? So there'd be an equal number of points.

 

[sman789]

infinity dosn't exist

 

[Kenny]

Originally posted by: KEV1N
Wouldn't the number of points on both segments have cardinality "R" (equivalent to the real numbers)? So there'd be an equal number of points.

Yeah that's what I'm thinkin.

 

[Vonkhan]

I rearended an Infinity today

 

[Nebor]

Originally posted by: sman789
infinity dosn't exist

Sure it does.... There an infinite number of points in a 1" line. There's .0001" and .0234544234" and .02042500000200000025". As long as you want to carry the place out. That's why there's infinite points.

 

[Vonkhan]

Originally posted by: Nebor

Originally posted by: sman789
infinity dosn't exist

Sure it does.... There an infinite number of points in a 1" line. There's .0001" and .0234544234" and .02042500000200000025". As long as you want to carry the place out. That's why there's infinite points.

people like u make my drunk noodle hurt

 

[Turin39789]

but the size of the points

 

[KEV1N]

Originally posted by: sman789
infinity dosn't exist

Infinity is a hard concept for humans to grasp.. I can't say anybody can really visualize an infinite amount of anything.

 

[Nebor]

Originally posted by: KEV1N

Originally posted by: sman789
infinity dosn't exist

Infinity is a hard concept for humans to grasp.. I can't say anybody can really visualize an infinite amount of anything.

I can... I just think of LCD related posts in the General Hardware forum.

 

[rob3rt]

they have the same # of points. the cardinality (size) of any two intervals on the real number line are the same. i remember learning this in college. basically you have to create a one-to-one mapping from the one inch segment to the two inch segment and vice versa. to go from one inch to two inch you take a random point in the one inch and you simply double it. if you want to go from the two inch segment to the one inch segment you have to devise a formula that will only give you a value between 0 and 1. i can't think of one from the top of my head but i'm sure its possible.

 

[sman789]

i'm just sayin, infinity cannot be reached

 

[TuxDave]

hmm... i think i'm beginning to see this cardinality thing but I have one question. So there's a way to do a 1 to 1 mapping, and I can think of a 1 to 2 mapping. Is the cardinality set by the lowest possible ratio?

 

[cheesewhiz]

there are an infinite number of sets of infinity.. if you can grasp that.. e.g., can you argue that the set of all numbers from 1 to infinity, incremented by 1, would be the same size as the numbers from 1 to infinity, incremented by 0.0000000000001, would be the same size? No. It's called 'infinite cardinal numbers' It's a concept that says (sorry, math majors ) infinity isn't the same number (since it doesn't exist in the context of a number system) for all sets.

 

[DogFromDuckhunt]

Originally posted by: Nebor

Originally posted by: sman789
infinity dosn't exist

Sure it does.... There an infinite number of points in a 1" line. There's .0001" and .0234544234" and .02042500000200000025". As long as you want to carry the place out. That's why there's infinite points.

No, infinity is an idea not a number. If you type out a real, actual number then its no longer an idea and you have put a value to it. You can approach infinity, you can get || that close to infinity, but you will never reach a non-existant number.

 

[Nebor]

I'm not gonna argue about it, but in my mind, I know I'm right.

 

[BurnItDwn]

Infinity is basicly a limmit.. There can be different levels of infinity. ie ... the sequences
Rn = R(n-1) + R^3
Sn = S(n-1) + S!
where n is all integers starting at 1 and approaching infinity ...

Sn / Rn is not 1 is it ??? no. also ... since N is approaching infinity ... will it ever be the same as Sn or Rn ... no.
So ... a Line has in infinite amount of greater points than a line segment since it has all the same points as the line segment in addion to all the points along that some line outside of the segment. It is infinitly longer.

 

[geno]

(they ARE equal, but post your comments to that in the other thread)

Why do YOU get to post YOUR comment here, but I can't? Screw you, I say they're not equal

 

Originally posted by: sman789
i'm just sayin, infinity cannot be reached

it cant be reached because its NOT a number, its a concept.

 

[OOBradm]

Originally posted by: Nebor
I doubt there will be two sides. If in any given line there are infinite points, then the length of the line is irrelevant. There are infinite points in a 1 inch line, and infinite points in a 2 inch line.