The notion of existence is applied to mathematical constructs so long as these constructs are abstractions/generalizations of things that exist in the physical

The notion of existence is applied to mathematical constructs so long as these constructs are abstractions/generalizations of things that exist in the physical world. The number two is a generalization of quantity. We know there may be two apples or two birds on the wire, and at one point we are taught quantity can be applied to virtually antyhing. Now, what's infinity? Another abstraction of quantity, which has many definitions. However, every definition you take involves infinite time, e.g. you add 1 to a number ad infinitum or you accelerate a particle to the speed of light, and because reaching precise speed of light is not possible, you will be doing it infinitely. So even "we use them to describe things we find in nature" - even that is not true. You can't find infinity in nature, neither anything that can be described with infinities.