Difference between revisions of "Empty set"

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In Set Theory, this is the only set that we know exists. All other sets must be formed using the Empty Set and a series of [[axioms]]. Thus, in a sense, the Empty Set is the basis of all [[mathematics]] as we know it - the "nothing" from which everything is formed.
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In Set Theory, this is the only set that we know exists. All other sets must be formed using the Empty Set and a series of [[axiom|axioms]]. Thus, in a sense, the Empty Set is the basis of all [[mathematics]] as we know it - the "nothing" from which everything is formed.
  
 
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[[Category:Set theory]]
 
[[Category:Set theory]]

Latest revision as of 20:33, 27 February 2020

The Empty Set (generally denoted $\emptyset$ or $\varnothing$) is the (unique) set containing no elements. It is therefore a subset of every set.


In Set Theory, this is the only set that we know exists. All other sets must be formed using the Empty Set and a series of axioms. Thus, in a sense, the Empty Set is the basis of all mathematics as we know it - the "nothing" from which everything is formed.

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