In the way of "Indexed"... A mathematical musing on faith

Thanks to the indexed blog for the inspiration.

Walking through campus the other day, I spotted the following message chalked all over our brickyard:

A) SCIENCE > RELIGION
B) RELIGION > SCIENCE
C) BOTH
D) NEITHER

This was followed by some pitch-line to attend a lecture or debate of some sort.

The real scary part about it is how quickly I came up with a retort. I've been so deep in theory for the past few weeks my mind started to work in notation, and before you know it, I had imagined the following answer:

D) NEITHER
Because SCIENCE ∈ ℝ and RELIGION ∈ ℂ and are therefore not directly comparable. Also, note that ℝ ⊆ ℂ. As such, ℝ ⋚ ℂ ⇔ any number z in ℂ has form α + βi where β = 0.

Simply stated, the two cannot be compared as they are in different sets. However, SCIENCE is contained in the subspace of RELIGION and the two are comparable iff the imaginary part is removed. Therefore, SCIENCE is a rational RELIGION that ignores the complex case presented by our own imagination.

After all, one has to imagine how imaginary numbers operate, it isn't intuitive. Ergo cognito et sum. My belief is based on faith. I visualize God and man in much the same way scientists imagine the real-complex plane. That is, a unit circle that is incomplete in the absence of i but that makes magical things happen when i is utilized.

Have some faith. Use your imagination, and realize you'll never fully understand with reason alone.