An Irrationally Radical Idea

Mother nature has been working to get southern California’s rainfall back up to average, and I’ve been working overtime to deal with it.  Consequently, I’m tired.  Jan made a squirrel, and I’ve dusted off an old favorite proof.

Irrationality of Non-Square Radicals

I was first introduced to this line of reasoning as a proof that is irrational.  However, the concept is easily generalized to all non-square radicals.  The proof follows the same reductio ad absurdum model, with the added assumption that . Continue reading

Rumble in the Trees of Midcity Park

for-the-love-of-nutsDawn broke, dew settled, and the thinning fog revealed an army of truth function pairs, more than two hundred fifty strong.  The crows sent a messenger; they came for war, and they would not rest until mathematical logic dominated our sovereign numbers.  We formed a defensive ring, and braced for the onslaught.

The hoard came all in one wave, tearing through additive and multiplicative closure like autumn leaves, before slamming hard against the associative and commutative properties of addition and multiplication. Continue reading