Recent content by g_edgar

When N=2 we have for example \varepsilon_{12}=+1. Now, you didn't define \varepsilon^{12} for us. Also, is there some Einstein summation convention in effect here?

You could, instead, do this: \frac{A}{x-1} + \frac{Bx+C}{(x-2)^2}. The point is that the numerator can be anything with degree less than the degree of the denominator.

the fact that circumference/diameter is the same for all circles is in Euclid, so it predates Archimedes.

Can you do these two Taylor series (at 0): (ln(1-z))^2 and 1/(1-z)^{m+1} ? Then take the product of the two series.

If a function is not one-to-one, then it has no inverse. Whether yours is one-to-one probably depends on the coefficients.

Power series is probably not useful. Your integrand |x|_p has only countably many values, and integrals of that kind are best converted to sums.

Actually, it is an equation, not a function. This equation can be used to define a function by someone who knows what he is doing.

When you say p-adic analysis, p is a prime, so p=0 is not used. |0|_p = 0. Sometimes the usual absolute value |x| is called the \infty-adic absolute value, and \infty is listed among the "primes". The p-adic absolute value is defined for the p-adic numbers, not the real numbers. Except the...

if I say to simplify, Maple it does

The covectors constitute the dual space of the vectors. This tells mathematicians how to treat them when you change variables. Physicists have these weird formulas to use for that... Why? You'll have to ask a physicist.

Woah, U^T in your formula and not U^* ... so in general U^T is not the inverse of U . Why did you choose that?

Wait: there's a bijection between the integers and the even integers, even though the big one has TWO copies (evens and odds) of the small one. Cardinality does these strange things.

What do you get if X_1 = X_2 = ..., which is sort of the EXTREME example of non-independence?

He writes $\int_R f(x) dx$ to mean the Lebesgue integral.

Nope. You have not proved the length of the circle (your limiting curve) is 4. You have proved, instead, that the length of the limit is not equal to the limit of the lengths. No need to use a circle to prove this: For example, you can use stairsteps converging to a sloping line segment.