How many subsets does a set #{{{O/}}}# have?

1 Answer
George C.
Nov 10, 2017

Two, namely:

#O/" "# and #" "{{{O/}}}#

Explanation:

The set:

#{{{O/}}}#

has just one element, namely #{{O/}}#

So it has exactly two subsets:

#O/" "# and #" "{{{O/}}}#

Bonus

Note that for any set #S# the power set of #S#, which can be written #2^S# is always larger.

Starting from #O/# we have:

#2^(O/) = { O/ }#

#2^(2^(O/)) = { O/, { O/ }}#

#2^(2^(2^(O/))) = { O/, { O/ }, { { O/ }}, { O/, {O/}}}#

#2^(2^(2^(2^(O/)))) = { O/, {O/}, {{O/}}, {{{O/}}}, {O/,{O/}}, {O/,{{O/}}}, {{O/},{{O/}}}, {O/,{O/,{O/}}}, {{O/},{O/,{O/}}}, {{{O/}},{O/,{O/}}}, {O/,{O/},{{O/}}}, {O/,{O/},{O/,{O/}}}, {O/,{{O/}},{O/,{O/}}},{{O/},{{O/}},{O/,{O/}}},{O/,{O/},{{O/}},{O/,{O/}}}}#

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