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January 31st, 2011, 10:09 AM   #1
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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.
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January 31st, 2011, 12:49 PM   #2
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Re: Binary Proof

It is true - any number can be expressed in base 2.
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February 3rd, 2011, 11:27 AM   #3
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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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