Math Forum / Mathematics / Undergraduate Math / January 2007

Let E and F be Banach space. Suppose E is compact and
T : E --> F be a continuous linear operator.
Then, is it true that both kernel and cokernel of T are finite
dimensional?

Hey guys!
Can anyone give me a hand on how to show this proof:
(A delta B) intersect C = (A intersect C) delta (B intersect C)
It's basically the distributive law for symmetric difference and

y' = -y/x -x/y
using the substitution y(x)= xz(x)
i get y= +/-  sqrt( (exp(4c) - 1 )/(2*x^4) )
as the general equation by seperation of variables.

I was recently in a class in which a teacher corrected a student who used "septagon" for the name of a seven sided polygon. I realized that the mixing of Greek and Latin terms might be an anathema to a language purist, but a teacher who had used triangle quadrilateral, and ...

Does there exist software to let me type out
mathematical equations on my laptop and print them out?
I am taking college level math and my handwriting is
terrible.... and when handing homework in is almost

how would you solve a diophantine equation of the form xyz.. = +/- n  ,
where n is an integer, x,y,z... being the variables
is there a general method for this specific form?
thanks

I need to find an example of an ideal of a ring which is a maximal
ideal but is not a prime ideal. I am thinking that, as a result of
Factor Ring theorems (If R is a commutative ring with unity that the
factor ring R/A is an integral domain IFF A is a prime ideal of R, and

f(z) is an entire function, and for all z,  |f(z)| != 1. Show that
f(z) is constant.
We didn't learn Picard's theorem, so I'm looking for another way of
showing this...

When integrating the complex function 1/( 2*sqrt(z) ) over the unit
circle ( |z| = 1), using Newton-Leibniz formula, why do I get different
results for different cuts?
Cutting along the positive real axis gives -2,

Hi, everyone
 I have trouble in solving an extreme problem.  I want to obtain the
upper bound of f(t) where
f(t)=(a1+a2*((d+r)^2-d*t^2/r)^k/2)/(d+r-t)    0<=t<=2r   k>=2.    Could

what makes a mathematical proof a proof?
during classes I allways hear: this is not a proof, when the the
theroem is being presented.
how do I know that something is a proof, and when it is just a

Machine Science [ Computer Science / Neuroscience / Computer Systems
Engineering ]
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Definitions

Reflection, Light & properties of "The Invisible" [ Physics ]
With equations that dealt with energy, matter and light at very high
velocities; let me give further meaning to
equations on matter/light and properties it/they assume at very high

Maths experts please help me with the missing numbers in the following sequence ;
72, 91, 103,____, 89,____, 96, ____, 72 (Fill in the blanks)
I have asked Dr. Math for help but unfortunately the doctors could not help me with this sequence.
Please send your answer to chustu@hotmail ...

I'm trying to prove two propositions:
1) Let there be a circle with two segments, BC and B'C',  that go
through the center of the circle, O, such that the angle between BC and
B'C' is 90 degrees. Pick another point on the circle, A, different from