Amazing facts you're pretty sure are true

[fluxquanta]

Originally Posted by missmilf25

yikes! um...how much 'younger' is 'younger'?

Probably about 12 years old.

[missmilf25]

Originally Posted by PoorGradStudent

Elephants are the only mammals that can't jump.

AND, according to mythbusters they ARE afraid of mice. who knew?

[Positive Control]

Originally Posted by DWarrior

Nope, not made up, it's a result of R and R^n having the same cardinalities.

For one example of a method that produces a unique single-coordinate identifier given two coordinates is this: imagine your X coordinate is .abcde... and your Y coordinate is .ABCDE... You can form a single real number that'll be unique to these coordinates: .aAbBcCdDeE... you thus have one coordinate that completely defines your position.

The pre-requisite for the above method is that each coordinate is some real number x so that 1>x>=0, but you can see that any real number can be uniquely identified by such coordinate using the same trick. For example, say X is a number ...EDCBA.abcde... and that it's either positive or negative, then your unique coordinate may be defined as .1aAbBcCdD... if X is positive, or .0aAbBcCdD... if X is negative or zero.

You can even extend it to all of space: X given by .abcde..., Y given by .ABCDE..., Z given by .klmno... your single coordinate is .aAkbBlcCm...

and so on. You can find other ways to uniquely represent stuff by one coordinate, and they'll all be fine as long as you use one method. As I said, it's not necessarily any more useful, but it's possible. It demonstrates that no dimension is "bigger" than another, they're all the same (as far as the number of points is concerned).

We use this all the time now in air travel. (Thought it is used for a two dimensional point on a map, not a three dimensional position of an aircraft with altitude.)

[Sparrow]

Originally Posted by fluxquanta

I'm aware of all of this, but you're not going to convince anyone who hasn't done a bit of general relativity or pure math of the fact that there are different types of "infinity", or that you can sort them in terms of cardinality. Especially not with Einstein summation notation. I hate that bullshit.

I..I think I just came?

[funnygurl1979]

Agreed Sparrow, Nerds Arguing nerd stuff is HAWT!

[hayroob]

Originally Posted by DWarrior

Nope, not made up, it's a result of R and R^n having the same cardinalities.

For one example of a method that produces a unique single-coordinate identifier given two coordinates is this: imagine your X coordinate is .abcde... and your Y coordinate is .ABCDE... You can form a single real number that'll be unique to these coordinates: .aAbBcCdDeE... you thus have one coordinate that completely defines your position.

The pre-requisite for the above method is that each coordinate is some real number x so that 1>x>=0, but you can see that any real number can be uniquely identified by such coordinate using the same trick. For example, say X is a number ...EDCBA.abcde... and that it's either positive or negative, then your unique coordinate may be defined as .1aAbBcCdD... if X is positive, or .0aAbBcCdD... if X is negative or zero.

You can even extend it to all of space: X given by .abcde..., Y given by .ABCDE..., Z given by .klmno... your single coordinate is .aAkbBlcCm...

and so on. You can find other ways to uniquely represent stuff by one coordinate, and they'll all be fine as long as you use one method. As I said, it's not necessarily any more useful, but it's possible. It demonstrates that no dimension is "bigger" than another, they're all the same (as far as the number of points is concerned).

Originally Posted by DWarrior

Countability doesn't stop at "uncountably infinite," so saying R and R^2 are uncountably infinite is not sufficient. For example, R^ω (infinite coordinates) is also uncountably infinite, but has a higher cardinality than R

In general, since the power set of A always has a higher cardinality than A itself, there is an infinite number of uncountable cardinals.

This is why I like DWarrior.

[DWarrior]

Originally Posted by funnygurl1979

Agreed Sparrow, Nerds Arguing nerd stuff is HAWT!

I think we were agreeing

[fluxquanta]

Originally Posted by DWarrior

I think we were agreeing

Yeah, what he said makes sense, I'm just saying that it won't make sense to many other people here, so I was effectively shitting over everyone else. I was having a graduate relativity flashback when you started throwing around R^ω, so I could've come off as a dickhead.

And yeah, I'm single ladies.

[DWarrior]

Originally Posted by Positive Control

We use this all the time now in air travel. (Thought it is used for a two dimensional point on a map, not a three dimensional position of an aircraft with altitude.)

For real? That would be baller.

[campy]

Originally Posted by PoorGradStudent

Elephants are the only mammals that can't jump.

They are also the only other mammal aside from Humans that have knees....or so i've heard