Homework Statement
I know this is the description of a bipartite graph:
A bipartite graph G is a simple graph whose vertex set can be partitioned into two mutually disjoint nonempty subsets V1 and V2 such that vertices in V1 may be connected to vertices in V2, but no vertices in V1 are...
I didn't even think to check it out that way. So with 32 inputs (domain) and 5 outputs (range), there's no way it can be one to one unless I'm missing something.
Now if it we're an encoding function where it would have to encode/decode back and forth, that would be one to one I think...
Homework Statement
I have a Hamming function which takes two inputs, domain & co-domain and the output is how many bits are different.
Example: f(11100, 11101) = 1 (only one bit is different).
Is this one to one?
I say no because there could be many other combinations if inputs that can...
Ha, I thought someone else posted in here too, but that was a different thread. Thanks to just you! Everyone else who will learn from this thread thanks you too! :approve:
Dam, I forgot to drop the +7 down on my notes. Either way I didn't even think to express +7 as
\frac{21}{3} . I keep learning something new every time I post to these forums.
Thanks Everyone!
Sorry to bring this post back up, but I'm not finding it so easy to do the inductive step. Can you or someone else let me know what I'm doing wrong.
A: (Basic Step)
Prove for n = 0:
e0= ##\displaystyle \frac{(4^{0+2}-7)}{3}## = 3 (Initital condition)
B: Assume n = k
ek=...
Thanks for the help. I simplified it to this:
##\displaystyle \frac{(4^{n+2}-7)}{3}##
I never realized their was so many ways that I could represent the same equation. The next part of my question is to prove it using mathematical induction so I want to make sure I have the simplest...
Homework Statement
The sequence {en} is defined recursively as e0 = 3; ek = 4ek-1 + 7, for all k ≥ 1. Use iteration to make an educated guess at an explicit formula for the sequence.
The attempt at a solution
I spent all day on this one and I'm still lost.
e1 = 4 x e0 + 7
= 4 x 3 + 7...
Ah, that's where the two came from. It cancels out the almost factorial :approve:
Thanks again for everyone's assistance. I like how everyone on here helps you figure out the answer for yourself, which is turn makes it's easier to understand come exam time.
Yes I can see how you did all the math to acquire the answer, but how you got the \frac{1}{2} confuses me a little. Is it because the question stated k ≥ 2 so you pulled it out of the factorial? Than you multiply both sides by 2 to isolate the nk.
Thanks for your patience with me!
Thanks for all the clarifications. I have been mixing up the terms and it's been hurting my grades.
so would it be
n_k = \frac{2}{(k+1)!}
Thanks. That's what I like about this forums. You can always count on everyone to correct all these errors. I have been learning a lot from them...
Sorry, I am trying to learn how to put the equations in using the correct symbols, so I forgot the parenthesis, which I know totally changes the equation. I meant the later..
n_k = \frac{(n_{k-1})}{(k+1)} ?