Recent content by Plato2

Have you tried to use induction ?

O.K. Admittedly we are making several assumptions about the setup (the wording) of your question. Both of us assume that there are two physicists who will not serve together, call them A & B. That means that any research group cannot have both A & B among the seven. Now a group can have A but...

$\dbinom{6}{3}$ is the number of ways to choose the mathematicians. $\dbinom{5}{2}$ is the number of ways to choose the two of the of the five cooperating physicists to put with the two who will not cooperate. In other words $\dbinom{6}{3}\dbinom{5}{2}$ is the number of team we do not want...

With no restrictions at all there are $\dbinom{6}{3}\dbinom{7}{4}$ ways to form the group. Now that are $\dbinom{6}{3}\dbinom{5}{2}$ ways to form the group with the two non-cooperative physicists together on it. But that is exactly what we must avoid. How do we use those two to answer the...

Use multi-set selections: Chose a four element multiset from $\{1,2,3,4,5,6,7,8,9\}$ That is $\dbinom{4+9-1}{4}=\dbinom{12}{4}=495$

There is no correct answer here. I don't agree with sentiments in reply #2. Here is my recommendation, a text by Larry Smith .

Re: Discrete Probability Quetion I do not follow that solution either. But here is a model. Think of a string 111000000000, the 1's represent the chosen lockers and the 0's empty. 100100000100 in that model no two chosen lockers are consecutive. But in 001000001100 in that model two chosen...

Well of course you can do do that, but why would you?

You have three cases: 1) $x\in (-\infty, N)$ then $|f(x)+5|<1$ implies that $|f(x)|<6$ 2) $x\in (N,\infty)$ then $|f(x)-5|<1$ implies that $|f(x)|<6$ 3) $x\in [-N, N]$ implies that $|f(x)|<B$

You do not have to be that abstract. Use the theorem: If f is continuous on [-n,n] then it is bounded there. From the given: $\left( {\exists {M_1} \in {\mathbb{Z}^ + }} \right)\left[ {x \geqslant {M_1} \Rightarrow \left| {f(x) - 5} \right| < 1} \right]$ & $\left( {\exists {M_2} \in...

Is it the case that \frac{n}{{\sqrt {{n^2} + n} }} \le {a_n} \le 1? Is {a_n} an increasing sequence?

This is a busy-work problem. Although I have not done the basic algebra, it appears that those two lines are skew lines. (you may need to show that) Two skew lines share a unique perpendicular. Its length is the diameter of the sphere. Now, one does not need to find that perpendicular. Just...

I remember that you have not studied De Morgan's laws. But I still do not understand your reasoning. Many, many years ago as a young assistant professor I was assigned to teach a foundations course. The department had chosen the textbook for the course before I was hired. In that text, the...

x\in(A\setminus B) means x \in A\, \wedge \,x \notin B. What is the negation: x \notin A\, \vee \,x \in B~~??

\neg \left( {x \notin B} \right) reads "It is not the case that x is not in B." That is a very stilted literal translation. How would one normally say that: "x is in B"??