Question 2 (a)
how is it possible? B is a set (since A is a set), how can a set be an element of another set?
Rather than saying: B is an element of C
I thought it would be better to say: B is a subset of C.
Also, can someone explain question 2 (d) to me? thanks
A first order DE models the rate of change, e.g. when decay is proportional to time we have the DE: dM/dt = -K.M; this is describing that rate of change mathematically. Am I correct in saying that a 2nd order DE describes the rate of rate of change?
Also, can anyone explain any application of...
I am studying Discrete Mathematics and if I do a PhD I would like to base the research on or around quantum computation. Unfortunately I can't take any physics modules at all, so please ignore the physics modules on the pages; I can only pick from the maths modules...
1 = 1
1 - 2^2 = -(1+2)
1 - 2^2 + 3^2 = (1+2+3)
1^2 - 2^2 + 3^2 - 4^2 = -(1+2+3+4)
and so on.
I have to prove that this relationship is true for all natural numbers. This is what I did:
clearly it is true for 1, 2, 3 and 4.
assume true for n odd:
1^2 - 2^2 + 3^2 - 4^2 ... + n^2 = (1 + 2 + +3...