The delta function only makes sense as a mathematical object when it appears inside an integral.
In the same way, there are other mathematical objects which may be considered as rings with extra structure.
This is to say that no mathematical object exists without human construction of it, both in mind and language.
What does it mean to refer to a mathematical object?
Since some theories are powerful enough to model different mathematical objects, it is natural to wonder about their own consistency.
Not our axioms, but the very real world of mathematical objects forms the foundation.
The games studied in game theory are well-defined mathematical objects.
These transformations are together described by a mathematical object known as a gauge group.
A number is a mathematical object used to count, label, and measure.
Such a circle of course cannot exist in the ordinary space we know, but as a mathematical object there is nothing wrong with it.