Hey I have 3 little simple math question if anyone can help. It’s just lines that I dont understand.

first

Y is a line in a complex plan that is determined by the origin and the complex number given by the scalar product of 2 vector x and y. It is denoted by (x,y)

Now sigma varies over the line Y’ (Y’ is symmetric to Y by the x-axis) so that sigma=tz (t is real)

z= complex conjugate of (x,y)(with the line over) / absolutevalue((x,y)). It is the unit vector

everything is good but now they say

sigma*(x,y)=t*abs(x,y). They say this is real. I dont understand

Second

E(j=0,p) = summation for index j from 0 to p

P^(j)(u) is a polynomial in u with power j

E(j=0,p)E(l=o,p) 1/(j!l!)*P^(j)(u)*Q^(l)(u)*(sigma-u)^(j+l) gives

E(k=0,2p) [ E(j=0,k (1/(j!(k-l)!)) P^(j)(u) Q(k-j)(u)] (sigma-u)^k

last

There exist an ‘‘n’’ so that (n-1)x is smaller or equal than… y… smaller than nx

for arbitrary x real positive and arbitrary y

now

h=b-a

n is greater than 1/h. 1/n is smaller than h

there exist an integer m such as

m/n smaller or equal to …a… smaller than (m+1)/n. (this is a modified version of the theorem above)

now ‘‘clearly’’ (well not for me)

(m+1)/n -a is smaller or equal to 1/n is smaller than b-a.

the right side of this is obvious (stated before) but I dont see why (m+1)/n -a is smaller or eq. than 1/n

sorry if this is not entertaining. I’ll post it in a math forum also.