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The well-ordering principle guarantees this by ensuring that any nonempty set of positive integers has a smallest element. Since the set of positive linear combinations is nonempty, it must contain a minimum value.
Conditions: Integers a and b are not both zero.; The set consists of positive values of the form au+bv where u and v are integers.
3:00 – 7:30Watch this moment ↗
The well-ordering principle guarantees this by ensuring that any nonempty set of positive integers has a smallest element. Since the set of positive linear combinations is nonempty, it must contain a minimum value.
Conditions: Integers a and b are not both zero.; The set consists of positive values of the form au+bv where u and v are integers.
3:00 – 7:30Watch this moment ↗