Hi,
first of all, Merry Christmas! I am doing some math while digesting another huge dinner, and have a small question.
Problem:
If A is any set of real numbers, define a function as follows:
Find expressions for and and
Attempt:
The way I am reading this, is that I first have to define a function which is 1 for real numbers, and 0 for pure imaginary numbers.
I think this one works fine:
where is the complex conjugate.
I am not so sure about the other expressions. If I still take B to be the set of pure imaginary numbers am I suppose to define the following functions:
Thank you for your time.
Because I am a fool.
Well, If x is in A and B, then and we are left with
If x is in A, but not in B then is not defined.
If x is not in A, .
The functions domain is x in A or B, so it is not defined if x is not in A or B..
If x is in A then and
I'm not very good at this...
Say A = 1,2,3,4,5 and B=3,4,5,6,7 then
= 1,2,3,4,5,6,7.
We want to remove the overlapping entries.
It makes sense if I think of as the probability of picking an entry from A or B..
is zero when and 1 otherwise.
Worst thing is, I was quite good at this a million years ago
Thank you very much.