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− | =[[HW1_MA453Fall2008walther|HW1]] | + | =[[HW1_MA453Fall2008walther|HW1]], Chapter 0, Problem 21, [[MA453]], Fall 2008, [[user:walther|Prof. Walther]]= |
==Problem Statement== | ==Problem Statement== | ||
''Could somebody please state the problem'' | ''Could somebody please state the problem'' |
Latest revision as of 16:48, 22 October 2010
Contents
HW1, Chapter 0, Problem 21, MA453, Fall 2008, Prof. Walther
Problem Statement
Could somebody please state the problem
Discussion
Using Binomial Theorem, $ (a+b)^n=\binom{n}{0}a^n+ \binom n 1 a^{n-1} b+...+\binom{n}{n}b^n $.
We have $ \binom{n}{0}+ \binom{n}{1}+...+\binom{n}{n}=(1+1)^n=2^n $
Using Induction
Base case:
n=0: $ 2^0=1 $ Subsets with 0 elements: {∅}
n=1: $ 2^1=2 $ Subsets with 1 elements: {∅}, {1}
So we can assume a set S with n elements has $ 2^n $ subsets.
n+1: $ 2^(n+1) = 2^1 + 2^n = 2*2^n = 2^(n+1) $
-Jesse Straeter