My goal: To show the dimension of space [itex]L[/itex] equals the length of any maximal flag of [itex]L[/itex];(adsbygoogle = window.adsbygoogle || []).push({});

Is the following valid?

My attempt:

Let [itex]M \rightarrow {L_{i-1}, ... L_i}[/itex]

where [itex]{e_i} \in L_i[/itex] [itex]|[/itex] [itex]e_i \not\in L_{i-1}[/itex]

Assuming [itex]e_i \in M[/itex] and [itex]e_i \not\in L_{i-1}[/itex],

we can say: [itex]e_i \in L_i[/itex] and [itex]L_i = M[/itex].

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

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

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

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