Rick Santorum I almost became a fan of Rick Santorum tonight.

[osan]

"Rights come from God... not from the state."

I know, I know. He's just pandering. But he seems like a smart guy, and this is one of the most intelligent things I've ever heard anyone beside Ron Paul say in the last two elections.

Without a definition of "god" the statement is nearly meaningless. It is a philosophical statement, whether or not is intended as such. Philosophical statements are by their nature non-casual and as such should be precise. Having proper and common definitions of terms is, therefore, essential if two or more persons are going to hold an intelligible exchange of ideas.

Given the circumstances under which the statement was made, replete with a lack of definitions, if one hundred million people witnessed his utterance I am confident that at least one hundred million and one interpretations were experienced. Taking such a statement loosely is not a wise thing and therefore should be disregarded no matter who makes them - unless of course the path forward includes a competent and thorough establishment of the common ground. That last bit is not mean feat.

All that aside, Santorum speaks out of his backside and I would not trust him to the end of his own nose because he believes in interfering in the lives of others. His rhetoric is rife with elements contradictory to what I would consider a proper stance on the question of human liberty. He is a war monger and would amount to nothing more than just another low-rent mass murderer in an expensive suit. I hold no doubt he would be more than willing to support and sign into law any bill that violated those human rights with which he disagreed.

I would not be too quick to dole out the praises based on sound-byte statements such as this. By this standard, Gingrich could be so credited, as could Romney, and incredibly even Obama on the rarest occasion. It is not terribly difficult to issue statements that, taken uncritically, may give the impression of great wisdom and emotional force. Close examination reveals such statements as nothing more than semantically empty strings of gibberish.

 

[PaulConventionWV]

http://math.about.com/od/geometry/ss/linessegments_2.htm quote: "A ray is part of a line. A ray will have one endpoint but will go on infinitely in one direction. A ray cannot be measured because it only has one endpoint."

No, a line is not larger than a ray, both are infinite.

ETA: Back to set theory, simply because it's easier to illustrate infinity in set theory.

The set [all real numbers] is infinite and represents a line. The set [all positive real numbers] is infinite and represents a ray.

That's my point. The "end point" of a ray doesn't actually have any meaning as it pertains to pointing out a beginning. If the ray truly is infinite, then either that point must be pushed back forever to extend it to the value of infinity, or the ray, going in one direction, must come back on itself to represent infinity, and in so doing, it must cross the original beginning point, meaning the point loses its representation as a beginning unless the point can be distinguished from other points on the endless ray.

Then again, maybe I'm just being devil's advocate.

 

[Mini-Me]

Lines and rays are both infinite, but lines are still arguably twice as long, because from a certain point of view, not all infinities are created equal. For instance, lim{n->0}2/n grows toward infinity twice as fast as lim{n->0}1/n. Dividing the former by the latter results in a quotient of 2.

It's also incorrect to state that a ray would have to somehow double back to its origin to be infinite. Dimensional "folding" would make such a loop possible, but even that would not cause the [still infinite] line to encompass "everything." After all, even a full line is only one-dimensional (even though it can cross any number of coordinate planes in n-dimensional space), whereas all of space is multi-dimensional. At the very least, the world we live in consists of 3 spatial dimensions...and probably more. However, the best example of disjoint infinite sets is probably the one Gunny gave (which I think was noting that the set of all even integers is infinite, and so is the set of all odd integers, but they don't intersect whatsoever).

 

[newbitech]

How so?

basic math

1/3 = .333~ (infinitely repeating 3)
3 * 1/3 = 3 * .333~
1 = .999~ (infinitely repeating 9)
1 > .999 (finite)
1 = infinitely repeating

if 0 = infinity and
1 = infinity
0=1? hmmm

 

[tttppp]

basic math

1/3 = .333~ (infinitely repeating 3)
3 * 1/3 = 3 * .333~
1 = .999~ (infinitely repeating 9)
1 > .999 (finite)
1 = infinitely repeating

if 0 = infinity and
1 = infinity
0=1? hmmm

That does not show 1=infinity.