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September 4th, 2015, 02:06 AM   #1
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Cardinality of generated sets

Hi , let $B$ be a Boolean algebra and $X \subseteq B$ a set. Can I proove that the cardinality of $X$ is the same as for the generated Boolean subalgebra by $X$ (that is: $\langle X \rangle = \{\bigvee_{i=1}^n \bigwedge_{j = 1}^{k_i} x_{j_i}^{\epsilon_{j_i}}: where \: x_{j_i} \in X \: and \: \epsilon_{j_i}= 1 \: or \:-1 \}$ )?
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