Finish the following proof for Theorem 1.4.12. Assume B is a countable set. Thus, there exists f : N -+ B, which is 1-1 and onto. Let A ~ B be an infinite subset of B. We must show that A is countable. Let nI = min{n EN: f(n) E A}. As a start to a definition of g: N -+ A, set g(l) = f(nI). Show how to inductively continue this process to produce a 1-1 function 9 from N onto A.

A is a countable set

Step-by-step explanation:

Assume B is a countable set, Go through the attached file for a detailed step by step explanation of the proof that A is a countable set.

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )