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diff --git a/Fourier Series.page b/Fourier Series.page
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@@ -106,6 +106,25 @@ This is the inner product of 2 real-number functions. For a function on complex
 The basis vectors of this Hilbert space are taken as follows:  
 basis vectors, $f_n = \frac{1}{\sqrt{2\pi}}e^{inx}$  
   
+Any basis vectors could conceivable have been assumed on the condition that the basis vectors are orthonormal. (*Note: These particular basis vectors are chosen to prove that Fourier series exists*)  
+  
+In order to prove orthonormality of the basis vectors:  
+  
+--> orthonormal proof goes here  
+  
+##Determining Coefficients of the Basis vectors
+In any vector space, the inner product of a vector and its basis vector gives the coefficient. For example, consider a 2-dimensional vector as shown below:
+
+--> image of a 2d vector
+
+--> demo of coefficient being true
+  
+Extending this principle to the case of an n-dimensional vector:
+--> compute inner product here and then continue to show what the coefficient formula is
+
+##Proving that this function is does indeed completely represent $f$
+
+--> don't quite remember this part
 
 #Why is Fourier series useful? </b>
 Applications will be covered on Monday July 5, 2010. See you all soon!  
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