Difference between revisions of "Empty set"
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| − | The '''Empty Set''' (generally denoted <math>\emptyset</math> or <math>\varnothing</math>) is the (unique) [[set]] containing no elements. It is therefore a [[subset]] of every set. | + | The '''Empty Set''' (generally denoted <math>\emptyset</math> or <math>\varnothing</math>) 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 | + | |
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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. | ||
{{stub}} | {{stub}} | ||
[[Category:Set theory]] | [[Category:Set theory]] | ||
Latest revision as of 20:33, 27 February 2020
The Empty Set (generally denoted 
or 
) 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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