$\"\"$

Given: $\"\"$

Prove: a is negative.

Indirect Proof:

Let us assume that a is non negative. $\"\"$

If we give possible non negative values to a, then

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ a is non negative \	\ $\"\"$ \
\ 0 \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \

This is contradiction because when a is non negative, $\"\"$ . $\"\"$

In both cases, the assumption leads to the contradiction of a known fact. Therefore, the assumption that a is non negative must be false, which means that a is negative is must be true. $\"\"$

The given theorem was proved that is a is negative.