[SOLVED] Symbolic difference?

Jan 2010
1
0
Does anybody know the difference between ⊔ and ∪ in a set-theoretic context? I've seen both symbols used in a solutions sheet I was provided with without any mention of the distinction between the two.
The answers relate to questions about order density in metric spaces which will eventually be applied to preference relations.

Many thanks

Edit: the equivalent is not true of the intersection (i.e. ∩ appears but ⊓ does not)

Edit2: Ok, for anyone who's interested or has the same problem as me I think I've worked it out - the square cup and square cap notation seem to be there in order to emphasize the fact that the union is over two different spatial dimensions. For example, in Euclidean space we would only use this if we are referring to the union of an interval on the x-axis and an interval on the y-axis, as opposed to the union of two intervals on the x-axis.
 
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Drexel28

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Does anybody know the difference between ⊔ and ∪ in a set-theoretic context? I've seen both symbols used in a solutions sheet I was provided with without any mention of the distinction between the two.
The answers relate to questions about order density in metric spaces which will eventually be applied to preference relations.

Many thanks

Edit: the equivalent is not true of the intersection (i.e. ∩ appears but ⊓ does not)

Edit2: Ok, for anyone who's interested or has the same problem as me I think I've worked it out - the square cup and square cap notation seem to be there in order to emphasize the fact that the union is over two different spatial dimensions. For example, in Euclidean space we would only use this if we are referring to the union of an interval on the x-axis and an interval on the y-axis, as opposed to the union of two intervals on the x-axis.
In my experience \(\displaystyle \cup\) is just meant to indicate union whereas \(\displaystyle \sqcup\) may be \(\displaystyle \amalg\) which is disjoint union. Des that sound right? Even this is uncertain though because techinically \(\displaystyle \coprod_{\alpha\in\mathcal{A}}X_\alpha=\bigcup_{\alpha\in\mathcal{A}}X_\alpha\times\{\alpha\}\) where most people use it just to symbolize that \(\displaystyle \left\{X_\alpha\right\}_{\alpha\in\mathcal{A}}\) is a pairwise disjoint class of sets.