Introduction to Set Theory (precursor to better evaluation of LA)

[CubicFlunky77]

My goal: To show the dimension of space L equals the length of any maximal flag of L;

Is the following valid?

My attempt:

Let M \rightarrow {L_{i-1}, ... L_i}

where {e_i} \in L_i | e_i \not\in L_{i-1}

Assuming e_i \in M and e_i \not\in L_{i-1},

we can say: e_i \in L_i and L_i = M.

Thus: {e_1, ... ,e_i} , {e_i} \in L_i = M \ L_{i-1}

for n = dim L or "finite dimension" of L such that: L_o \subset L_1 \subset L_2 ... \subset L_n

 

[micromass]

What are $M$ and $L_i$?

 

[CubicFlunky77]

I apologize for posting in a rush.

L is a maximal flag defined by L_0 \subset L_1 \subset L_2 ... and L_i is a space for which ({e_1, ... ,e_i}) forms the basis. Assuming
({e_i, ... ,e_{i-1}}) is valid, M is a linear span of the aforementioned basis of L_i.

 

[CubicFlunky77]

Help... anyone? :(