define the term empty set
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Definition
The empty set is a set which has no elements.
It is usually denoted by some variant of a zero with a line through it, for example ∅∅ or ∅∅, and can always be represented as {}{}.
Axiomatic Set Theory
The concept of the empty set is axiomatised in the Axiom of the Empty Set in Zermelo-Fraenkel set theory:
There exists a set that has no elements:
∃x:∀y:(¬(y∈x))∃x:∀y:(¬(y∈x))
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The term 'empty set' is a term which can be defined as a set having no element.
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