Did you guys know there isn't a surjection from a set to its Power set. ZING.
Name:
Anonymous2006-05-25 15:43
cool!
for your next assignment prove that if f is L^2 and its fourier transform F is L^1 then f equals integral of F(t)e^ixt dm(t) over R almost everywhere.
Name:
Anonymous2006-05-25 15:57
Pope Sixtus V limited the number of cardinals to 70 (six cardinal bishops, 50 cardinal priests, 14 cardinal deacons). In 1975, Pope Paul VI created the age limit on electors and raised the limit to 120 cardinal electors. But the numerical limitations have been frequently disregarded in order to make the College of Cardinals a more representative body.
>>1
it's a basic theorem of abstract set theory...
"2^x>x whenever x is a cardinal number"...
if you find a surjection from a set to it's power set, that would imply that the cardinal of the set (say x) is greater then or equal to the cardinal or it's power set (which is 2^x).... that contradicts the theorem and hence leads to the failiure of set theory...
What will you give me if I did? Here is a hint for you. Suppose there is a surjection f from a set X to its power set P(X), now look at the set
S={x in X such that x is not in f(x)}