Direct Proof/Examples/Greater Than

Example of Direct Proofs

Let it be assumed that:

the greater than relation is transitive.

the two premises $12 > 10$ and $10 > 8$ both hold.

Then the following is a direct proof that $12 > 8$:

\(\ds 12\)

\(>\)

\(\ds 10\)

by hypothesis

\(\ds 10\)

\(>\)

\(\ds 8\)

by hypothesis

\(\ds \leadsto \ \ \)

\(\ds 12\)

\(>\)

\(\ds 8\)

greater than is transitive by hypothesis

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): direct proof
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): direct proof