## Twitter proof: size of the set of subsets of a set

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Let's prove that, if a set has size $$n$$, then that same set has exactly $$2^n$$ subsets.

Take a set of size $$n$$. For any of its subsets, we can label items with $$0$$/$$1$$ depending on whether or not the item is in the subset or not, and to any such labelling corresponds a single subset. There are $$2^n$$ such labellings, hence $$2^n$$ subsets.

Do you have an idea for a twitter proof? Let me know in the comments below!