In Being and Event Badiou defines $\in$ as the sign of belonging. Belonging is equivalent to presentation. Imagine a situation-set called $VFC$, also shown as a diagram: Situation-Set VFC .
In this case $\beta$ belongs to the situation-set $(\beta \in VFC)$ (i.e. is presented), and $\alpha$ is included $(\alpha \subset VFC)$ in the situation-set (i.e. is represented).
We know that whatever is represented (i.e. included) also belongs to the power-set (i.e. the metastructure of $VFC$) which is written $P(VFC)$.
So we can say $\alpha \subset VFC$ but also $\alpha \in P(VFC).$
Now my question is, how do I draw the correct diagram of $P(VFC)$? Is it: Power-set of VFC.
Now for $\beta$, in words, Badiou states that $\beta$ belongs to the situation-set $VFC$ (presentation) and is equally included (representation).
So according to the attached diagrams we have $\beta\in VFC$ but also if $\beta\in P(VFC)$ then $\beta\subset VFC$, so we have both $\beta\in VFC$ and $\beta\subset VFC$? Is that correct?
Badiou says this term is a normal term, i.e. $\beta$ is normal term, in contrast to $\alpha$ that is a excrescence term (represented but not presented).
But how does that make sense w.r.t. the diagrams, what is not consistent here? The maths? The words? The diagrams? How can $\beta$ both $\in$ and $\subset$, how does that make sense with the diagrams?