On Wednesday night when I was walking back from orchestra, some journalist stopped me and asked me to give a quote for the newspaper. He asked whether I would rather be in class or at the beach on such a nice day. I told him that I would rather be in class since I don’t like beaches. That was quite a silly thing to say, but I didn’t have a lot of time to come up with something decent. Apparently my quote showed up in the newspaper yesterday, but I haven’t verified this independently since I don’t read the newspaper. Scharlemann told me at tea yesterday that he was happy that I had said that since I might have been referring to his class.
Some fellow believes that he has proven that ZF- is inconsistent. However, it appears that the paper is flawed.
And now for a problem (which has not been stated in a well-defined manner yet by me): Suppose we are given a power series centered at 0 with radius of convergence r>0. Now select a complex number z with |z|>r. In terms of the power series coefficients and z (I suppose), what is the density of the smallest number of coefficients we must change in the power series to make the power series converge at z?
Clearly, changing a finite number of terms will never make any difference, and using the formula for the radius of convergence (which I had forgotten when I started thinking about this problem), we can see that if the coefficients are in a geometric progression, then we must modify all but a finite number of terms. What happens in other cases?