Recent content by cordyceps

All that was given in the textbook was a proof of the cauchy-schwarz inequality. The binet-cauchy identity, which was used in some of the proofs I glanced at, was never mentioned.

Homework Statement Prove Lagrange's identity for real numbers http://mathworld.wolfram.com/LagrangesIdentity.html The Attempt at a Solution I tried one of the methods used in proving the Cauchy-Schwarz inequality (Ax^2 + Bx + C is greater than or equal to zero, where a = the sum from...

Great idea! I just remembered a little of dedekind on irrational numbers, but his proof that the set of rational numbers is uncountable is pretty long. Do you know a shorter method? And where would you start for the contradiction method? Thanks for the reply.

Have you tried manipulating the expression (2n+3)/(3n+6)? Separating the expression into two fractions might help.

RSI takes incoming seniors.

Homework Statement Given any real x > 0, prove that there is an irrational number between 0 and x. Homework Equations I'm not sure if the concepts of supremums or upper bounds can used. The Attempt at a Solution Take an irrational number say Pi. We can always choose a number n such...

RSI's focus includes math and engineering. Not to discourage, but RSI is one of the most difficult programs to get into. I think around 80 juniors every year are selected. Here's the link: http://www.dodea.edu/students/rsi.cfm From what I remember, RSI required a minimum score of 220 on the...

I was in a similar position last year- our class covered Newtonian mechanics and EM, while thermodynamics, optics, hydrostatics, etc. were ignored. Now if you've taken AP's before, you already know that AP exams are curved significantly. For physics B, you can study a little extra, score 50-60%...

So, for the non-empty set S of positive integers, one of the relations x < y or x > y holds between any two members. This means that each member in S is greater than or less than each of the other members. Also, if some member x of S is less than some member y, and y is less than some member z...

Oh, also some of the field axioms for real numbers: 1. Exactly one of the relations x = y, x < y, x > y holds. 2. If x > y and y > z, then x > z.

Sorry for the late reply. I have the definition of an inductive set and the definition of a positive integer: a real number which belongs to every inductive set.

Homework Statement Prove that every nonempty set of positive integers contains a smallest member. This is called the well-ordering principle. The Attempt at a Solution I'm just starting out with analysis, so I'm not too sure about the format of proofs. Here goes: Proof. First suppose...

Our Physics C: Mechanics class uses calculus rather conservatively. The calc we used primarily involved separable differential equations and one-variable integration, topics you can quickly learn. Perhaps the only topic in Physics C which requires a more solid grasp of calculus is harmonic...

I don't think many schools would allow students to skip Calc AB and go straight to BC. But I agree that Physics C would be a better choice than Physics B. Physics B covers mechanics and EM at a very basic level.

That looks very doable. In fact, if you find some extra time on your hands, maybe you could grab a calc book by apostol or courant for self-study.