Question
Given that a line has infinite points (if it has less I'd like to know the number):
- which is larger, the amount of points on the line or the amount of points in a solid square which is the area line^2?
Or do they both have the same amount of points?
Recognized Member
*head explodes*
PG, at least let me finish my morning coffee before I have to ponder stuff like this.
Hello Pika Art by Dr Unne ~~~ godhatesfraggles
I would say a line because it doesn't end, unlike a square (or cube for that matter), which does have a specified limit as far as dimensions are concerned. Even if the square were big, the line would eventually get to a point where it surpasses the square, despite how long it would have to be.
However, for what you are asking, both of them are undefined, since you let the line go on forever, and are building a square around it. Since infinity times two is still infinity, neither are larger. Concept + numbers = lose.
No the line has a fixed length.
The square, then. Since it's line^2, which is obviously more than X. It's not infinite if it has a fixed length.
There are an infinite number of points in a line, and an infinite number of points in a plane, whether the line / plane are bounded or not. So the only question is how do you compare their infiniteness to each other?
From what I remember of number theory, the set of real numbers is an uncountable infinity. The number of points in a bounded line maps to the set of real numbers. The number of points in a bounded plane seems (without giving it much thought) like it also maps to the set of real numbers. I would guess that they have the same sort of infiniteness: uncountable infiniteness.
This kind of thing can be counter-intuitive. Like, if you compare the set of all integers, with the set of all even integers, it turns out they have the same size; they are both countably infinite. "Size" is defined differently for infinities than it is for actual numbers.
("Countable set" means that the set can be mapped to the set of natural numbers. http://en.wikipedia.org/wiki/Countable_set )
My head just burst, i have no idea
The square is infinite to the power of 4. So technically greater than the line but both would go on forever so technically they are the same.
yay for Dr UnneOriginally Posted by Dr Unne
I suck at math. Does that help?
For practical purposes infinity is infinity no matter which way you look at it.
However there are greater amounts of infinity as we have illustrated, though the metaphor is misleading: infinity isn't a number.
Right, it's like asking if there are more whole numbers (1,2,3,4...) or more even numbers.
There are more whole numbers than even numbers. Both have infinite amount of numbers though.Right, it's like asking if there are more whole numbers (1,2,3,4...) or more even numbers.
A line is more versatile, so I'll go with that. >_>
I sux at math.
Posting Permissions
Reply With Quote
