Prove n-cube is connected for n >= 1 (Hint: Induction)

[hyderman]

Prove that the n-cube is connected, for n ≥ 1.

(Hint: build the n-cube using two copies of (n − 1)-cube and use induction on n.)

how do you solve that ... please explain in steps thanx

 

[stapel]

how do you solve that

Are you not familiar with induction proofs?

please explain in steps

Most legitimate tutors don't always give complete worked solutions. It would probably be good if you started showing some work of your own. (If you can't even get started on this exercise either, then perhaps a conference with your academic advisor is in order.)

Thank you.

Eliz.

 

[pka]

Look at the two 2-cubes at the top.
The next step is a 3-cube.
How did we go from 2 to 2+1?

 

[hyderman]

whats you saying is that from 1-cube ...you build a second 2-cube .... thats fine so
so n-1-cube should be (x1, x2, ..., xn-1, 0)
and 2-cube should be (x1, x2, ..., xn-1, 1)

i understand that so by induction how to build the steps.... we are not taking induction this is just a question to test our knowledge in cubes and gaphs.....