Haha, keep doing combinatorics and a lot of stuff will blow your mind.michonamona said:Homework Statement
Why is the size of the power set 2^n ?
To elaborate, suppose we have a set B that has n elements. Let C be the set that contains all the possible subset of B. Why is it that |C|=2^n ?
It boggles my mind why the base is 2 for all size of sets.
Thank you,
M
Homework Equations
The Attempt at a Solution
michonamona said:Homework Statement
Why is the size of the power set 2^n ?
To elaborate, suppose we have a set B that has n elements. Let C be the set that contains all the possible subset of B. Why is it that |C|=2^n ?
It boggles my mind why the base is 2 for all size of sets.
Thank you,
M
Homework Equations
The Attempt at a Solution
The size of the power set is determined by the number of elements in the original set. If a set has n elements, its power set will have 2^n elements.
To calculate the size of the power set, you can use the formula 2^n, where n is the number of elements in the original set. For example, if a set has 3 elements, its power set will have 2^3=8 elements.
A set is a collection of unique elements, while a power set is a collection of all possible subsets of the original set. The power set includes the original set, the empty set, and all possible combinations of elements from the original set.
Yes, the size of the power set can be infinite, depending on the size of the original set. For example, if the original set has an infinite number of elements, its power set will also have an infinite number of elements.
The size of the power set is important in mathematics because it allows us to understand the number of possible combinations and subsets of a given set. It is also used in various mathematical concepts and calculations, such as probability, combinatorics, and discrete mathematics.