Existential Import/Examples/Reducible Fraction

Example of Existential Import

The statement:

Some fractions are reducible

is assumed to have existential import.

Proof

The statement is equivalent to:

There exists at least one fraction which is reducible.

This becomes false if there does not exist a reducible fraction.

$\blacksquare$

Sources

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