.. title: What is the proof that total number of subsets of a set is 2^n?
.. slug: what-is-the-proof-that-total-number-of-subsets-of-a-set-is-2n
.. date: 2019-01-29 05:18:44 UTC-08:00
.. tags: maths
.. type: text
.. has_math: yes

I have known "by heart" that total number of the subsets of a set of n number is :math:`2^n`
I was struggling to find an intuitive explanation, and two answers helped me to understand it.

    For each element, you have two choices: either you put it in your subset, or you don't; and these choices are all
    independent.

Citation:

Bruno Joyal (https://math.stackexchange.com/users/12507/bruno-joyal), What is the proof that the total number of
subsets of a set is $2^n$?, URL (version: 2013-10-31): https://math.stackexchange.com/q/546417

Another was this table that represented the sets as binary, to denote 0 as an absence of the element and 1 as presence
of the element.

.. image:: https://dl.dropbox.com/s/0smcrv98o8igrhh/power_set.jpg


That can help us understand that the total number of subsets of set of n is :math:`2^n`