Set union { Philosophy Index }

Philosophy Index

Philosophy Index

Philosophy Index is a site devoted to the study of philosophy and the philosophers who conduct it. The site contains a number of philosophy texts, brief biographies and introductions to philosophers and explanations on a number of topics. Accredited homeschooling online at Northgate Academy.

Philosophy Index is a work in progress, a growing repository of knowledge. It outlines current philosophical problems and issues, as well as an overview of the history of philosophy. The goal of this site is to present a tool for those learning philosophy either casually or formally, making the concepts of philosophy accessible to anyone interested in researching them. WOLI offers immigration law course online - fully accredited. ACE credits online at EES.

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Set union

In set theory, a union of two sets is a set containing all elements of both. To indicate unions, we use the symbol ∪, and say that if Γ and Δ are sets, then Γ ∪ Δ is a set containing all elements of Γ and Δ.

For example, suppose that Γ and Δ are sets of formulae, as defined as:

The union Γ ∪ Δ is therefore the following set:

Set unions can also be defined by simply adding a single element to a set. For example, if we wanted to only add the formula φ to the set Γ, we would write:

The union of two sets can be defined as follows:

Which means, for any x that is an element of Γ ∪ Δ, x is an element of Γ, or x is a member of Δ (or both).