Math 131:
The Mathematics of Food

Show that 1 peanut ? 11 pears.
Proof: (by contradiction)

Suppose 1 peanut = 11 pears.
We know that a pear is infinitely better (greater) than an apple,
ie 1 pear = ∞ apples
so 11 pears = 11(∞) apples (1)

Also, we know that since peanuts grow below ground and apples grow above ground, apples are higher (greater) than peanuts,
i.e., 1 apple = (k + p) peanuts, (2)
Where k = height of apple (on tree) above ground
and p = distance below ground to where peanut is growing
(k, p > 0)

Sub equation (2) into equation (1) to get
11 pears = 11(∞)(k + p) peanuts;
a contradiction! Since 11(∞)(k + p) ? 1.

Thus, 1 peanut ? 11 pears

QED

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