# Recent content by g_edgar

1. ### Product of Two Levi-Civita Symbols in N-dimensions

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?
2. ### Concept Decomposing of Partial Fractions

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.
3. ### How to measure perimeter without pi?

the fact that circumference/diameter is the same for all circles is in Euclid, so it predates Archimedes.
4. ### A weird equation to solve

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.
5. ### Inverse function in one dimension

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.
7. ### Is this considered as a function?

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...
9. ### A Function to Integrate

if I say to simplify, Maple it does
10. ### Are the definitions of vector in Linear Algebra and physics compatible?

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.
11. ### Diagonalization of complex symmetric matrices

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?
12. ### Number of points on the plane vs. number of points on the line

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.
13. ### Give an example to show that if not assuming independence of

What do you get if X_1 = X_2 = ..., which is sort of the EXTREME example of non-independence?
14. ### Convolutions of Lebesgue integrable functions

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