They are factual whether they are experienced or not. This many *** ** and this many ***** are the same. A thing is the thing that it is. That is pure logic. It might even be the most fundamental principle of existence.
It is indeed a fact based on reality, but it needn't be true or even have meaning in a mathematical system.

Reality is real; mathematics as an entity is not. There is no such thing as a 'mathematical number' as opposed to a 'real number', there are just numbers. Numbers of real, physical objects or properties of objects.