The only popular counterexample is the integral transform
A real number can be defined by what rational numbers it is less than, or by what rational sequences converge to it, but the choice of construction soon stops making a difference. It is common for a theorem to screen off the details of a definition.
A real number can be defined by what rational numbers it is less than, or by what rational sequences converge to it, but the choice of construction soon stops making a difference. It is common for a theorem to screen off the details of a definition.