Recent content by Thetes

In vector calculus, dimensions are broken up into independent components. But a vector has "length" and "direction", so it's not just a point in space. It has an associated length in whatever dimension the space you are looking at (for a cube then 3 dimension). Now, all these ideas become even...

http://larouchepac.com/node/22355 (NAWAPA) originally proposed in 1964. [SIZE="1"]"Every Member of Congress, everyone in the executive branch from the President on, in the field of national resources, has to plan during their period of administration or office for the next generation, because...

Mark44, You are in good company! Qualitative and quantitative changes are a vast subject of debate among reductionists and scientists. Qualitative changes will lead you into a better understanding of geometry and the complex domain. Just a little from Leibniz from here...

Greetings, I can't tell if that quantity below the problem is part of the divisor or just something extra, but distribute the quantity into the right side of the equation. Then move the term with the same exponent over to the left. Now you can take the natural log of both sides. Just needed...

The closer you look at the foundation the more wobbly it seems. Set theory is how number systems are defined. But, this is like a shell game. You ask what is a number, so I tell you well it's made of smaller objects. Then you ask what are the smaller objects. So, I quit hiding behind...

There is nothing bogus about asking what a number is. It's a valid question and something that is hidden from most people that use math. Thehttp://www-math.mit.edu/~katrin/100/notes/natural.pdf" is from set theory. You have to have axioms and the inductive property and you can build the...

Avatrin, Sorry I glossed over the important part. If I understand correctly, you would like to see the proof of the application of the characteristic polynomial solutions. http://condor.depaul.edu/ntomuro/courses/415/notes/lecture8.html" starts the proof and continues with the cases. It's...

Avatrin, Recurrence relations are a way to express a function by using that same function in it's definition. There is usually a base case (at least in any I can remember). Then the solution set can be built iteratively. Take the Fibonacci sequence: 0,1,1,2,3,5,8,13, etc The sequence is...

It's not an implicit assumption. It's the stated premise. Perhaps we just have different interpretations of the original question. And I by no means claim to have an authority on what they originally were. If we are talking about the dichotomy, then the premise is continuous space and...

Thanks for the opportunity to clarify, calculus has nothing to do with the validity of the paradoxes. Using limits means we are assuming continuity and thus infinite divisibility, exactly what Zeno paradoxes are about. So, it tells us to look at his continuous motion paradoxes [the dichotomy...

A good question! And one that has been around since ancient times. An Ionian Greek thinker Zeno proposed a number of paradoxes that while taken into consideration may well have predicted our uncertainties of motion and position: http://www.mathpages.com/rr/s3-07/3-07.htm The argument goes...

Thanks for the references, and sorry I left out a term (G) in the original equation as well.

Greetings! Would this be a fair estimate to the radius of a black hole? Assumptions: The equation for escape velocity is adequate for calculation of black hole radius. \upsilon = \sqrt{\frac{2M}{r}} Working from there, setting the desired velocity faster than light would mean nothing could...

It doesn't even make sense to question the existence of existence.

I was implying that when a contradiction is taken as premise, then anything can be the result.