Recent content by gutnedawg

are you saying that since A in V_b and A in V_a then for all V_b in V_a -> V_b is contained in V_a

how do I apply the induction hypothesis?

alright well TI was one of my questions that I had so I'm glad you typed this out -V_0 = the empty set which is transitive since y in V_0 is the empty set and the empty set is contained in the empty set -V_a+1 I'm not sure, I know I have the power set in my notes I just can't find them right...

alrighty, now for V_alpha V_alpha={a : rk(a)<alpha} let rk(V_beta)= beta for all beta<alpha then V_beta is in V_alpha for every beta<alpha by the definition of V_alpha do I just do the same thing as I did above pick a gamma and solve?

for some reason Latex is giving me grief for a gamma in beta we have gamma<beta<alpha and thus gamma in beta in alpha then gamma is in alpha meaning that beta is contained in alpha is this a sound demonstration? \gamma \in \beta \gamma <\beta<\alpha \gamma...

I was in a hurry so I meant to type out beta instead of B each ordinal \alpha is the set of all smaller ordinals i.e. \alpha = {\beta : \beta<\alpha

my definition is each ordinal a is the set of all smaller ordinals, i.e. a={B: B<a} this mean B ε a I'm not sure how to get the inclusion, I mean I know that B is included in a but is this obvious or should I show this?

Homework Statement show every ordinal is a transitive set show that every level V_a of the cumulative hierarchy is a transitive set Homework Equations The Attempt at a Solution I understand that these are transitive sets, I'm just not sure how to show this. I feel like the...

what I was thinking is incorrect... I'm just not seeing a pattern that would give me what I need

I think it's N_p+m correct?

Yea this was what I was trying to get at however you put it much more elegantly... My question before was how could I 'count' the number that come before m/n in a specific p. IE 3/1 is at position 5 we know p=2 + p=3 =3 but how can I include the fact that 1/3 and 2/2 come before 3/1 within the p=4

could I write that: m+n=a_j and call this a set with a_j elements then create a position set {{1/1},{1/2,2/1},{1/3,2/2,3/1},...} that is a_0,a_1,a_2 etc... the position would be the addition of the number of elements in a_0+a_1+a_2... I don't know where I'm going with this

Homework Statement Prove that the fraction m/n occurs in position \frac{m^2 +2mn + n^2 - m -3n}{2} of the enumeration {1/1, 1/2, 2/1, 1/3, 2/2, 3/1,...} of the set Q+ of positive rational numbers. (Hint: Count how many terms precede m/n in the enumeration.) Homework Equations The Attempt...

so lanedance I can just say that if x\cap z = z then the first equality holds?

Homework Statement describe exactly when x intersecting (y union z) = (x intersecting y) union z Homework Equations The Attempt at a Solution I just for some reason cannot see this solution and need a shove in the right direction