Subject: How can purple exist?

Full Question:
When dealing with colors, I often think in terms of three primary colors being 
mixed on a color wheel.  However, I know that the colors my eyes see are 
actually light waves of different frequencies that can be represented on a color 
spectrum.  For this reason, I like to visualize the ends of the spectrum 
connected to form a wheel.  But, if the color wheel comes from the looping of a 
spectrum rather than the mixing of colors, where does purple come from?  Why 
should mixing red and blue light create light with a higher frequency than 
either color, when mixing red and yellow light or blue and yellow light creates 
a color with a frequency somewhere between the two colors?

Re: How can purple exist?