diff --git a/_posts/2019-02-15-ch2-notes.md b/_posts/2019-02-15-ch2-notes.md
index fd0bb2063899e821e76b4362a13ac08ca32bfd66..8578eb08e163ddd5c53676ea0de37f54f65f0520 100644
--- a/_posts/2019-02-15-ch2-notes.md
+++ b/_posts/2019-02-15-ch2-notes.md
@@ -30,7 +30,7 @@ $$
 $$
 
 The Fourier Inversion Theorem states that $$\mathcal{F} \mathcal{F}^{-1} = \mathcal{F}^{-1}
-\mathcal{F} = \mathbb{1}$$ (where $$\mathbb{1}$$ is the identity operator). This holds for the space
+\mathcal{F} = \mathcal{I}$$ (where $$\mathcal{I}$$ is the identity operator). This holds for the space
 of functions whose Fourier transforms exist and for which both the function and the transform are
 absolutely integrable and continuous. All claims I make about functions should be interpreted to
 apply only to functions in this space.
@@ -77,7 +77,7 @@ $$
 Thus $$\mathcal{F}^{-1} = \mathcal{F} \mathcal{R} = \mathcal{R} \mathcal{F}$$. This means that
 
 $$
-\mathbb{1}
+\mathcal{I}
 = \mathcal{F} \mathcal{F}^{-1}
 = \mathcal{F} \mathcal{F} \mathcal{R}
 = \mathcal{R} \mathcal{F} \mathcal{F}
@@ -86,7 +86,7 @@ $$
 and
 
 $$
-\mathbb{1}
+\mathcal{I}
 = (\mathcal{F} \mathcal{F}^{-1}) (\mathcal{F} \mathcal{F}^{-1})
 = \mathcal{F} \mathcal{F} \mathcal{F} \mathcal{F}
 $$
@@ -138,6 +138,7 @@ In this version horizontal arrows indicate Fourier transforms (and you can alway
 a horizontal arrow by taking the inverse Fourier transform), and vertical arrows indicate complex
 conjugates.
 
+
 ### Even More Odd
 
 Recall that a function $$f$$ is even if $$f(-x) = f(x)$$, and odd if $$f(-x) = -f(x)$$. Note that a
@@ -148,5 +149,21 @@ hold, we can deduce some interesting things from the commutative diagram above.
 - a function is even $$\iff$$ its Fourier transform is even
 - a function is odd $$\iff$$ its Fourier transform is odd
 - a function is real $$\iff$$ the conjugate of its transform is its inverse transform
+  $$\iff$$ conjugating its transform is the same as flipping its transform
 - a function is real and even $$\iff$$ its transform is real and even
 - a function is real and odd $$\iff$$ its transform is imaginary and odd
+
+The case where $$f$$ is a real function is used often enough to be worth drawing out explicitly. It
+also helps see the the cases for even and odd real functions. Here the diagonal arrows represent
+Fourier transforms (as always they can be inverted), and the vertical arrow represents the complex
+conjugate (which in this particular case is equivalent to the flip operator).
+
+$$
+\begin{array}{rcccl}
+&& \hat{f}(x) = \overline{\hat{f}(-x)} && \\
+& \nearrow && \searrow & \\
+f(x) && \updownarrow && f(-x) \\
+& \nwarrow && \swarrow & \\
+&& \overline{\hat{f}(x)} = \hat{f}(-x) &&
+\end{array}
+$$