January 31st, 2011, 10:09 AM  #1 
Member Joined: Jul 2010 Posts: 42 Thanks: 0  Binary Proof
Any number "n" can be expressed as either the sum of powers of 2 or a single power of 2. Both and are valid to the assertion. With n as any number, we have... Case 1: By definition of where Case 2: (satisfies assertion) Case 1 continues the pattern as you substitute in for . The pattern follows that for each substitution into , another sequence of powers of s will be transformed into the equation. The pattern follows this ultimate equation: Thus proving that for any given valid entry for any variable, n can always be expressed as the additive sequence of a power of s. 
January 31st, 2011, 12:49 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,768 Thanks: 699  Re: Binary Proof
It is true  any number can be expressed in base 2.

February 3rd, 2011, 11:27 AM  #3 
Member Joined: Jul 2010 Posts: 42 Thanks: 0  Re: Binary Proof
My apologies, I'm well aware that any number can be expressed in the base of 2, or any base for that matter. I'm interested in whether or not the proof works and makes sense. 

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