Multiplication and OCD

Hi,

I have a thought bothering me. I consider a number to be an abstract quantity. If so, then addition or subtraction of abstract quantities results a new abstract quantity. For multiplication, obviously an abstract quantity multiplied by another results a product; the multiplier is an abstract quantity and so is the multiplicand. What is bothering me is this: when doing multiplication, one provides an instance for the multiplier, for example 3*5 means three-fives; both 3 and 5 are abstract quantities and so is their product; three-fives instantiates number three. So doing multipication, you provide an instance for the multiplier and then get the product. I don't know how to further express myself.

I need help with this, otherwise it's an obstacle for me. I can't study something else in math since this thought and uncertainty are bothering me. I need somebody to reassure me of whether the thinking is correct or not. Thanks for reading.

I followed you until three-fives instantiates number three. You could think of it as three-fives is just another abstract just on another level. like 2d vs. 3d. or in my mind, I layer them. 5 on 5 on 5. I think it has more to do with the 5 than the 3.

Any element in the set of integers, when added or multiplied to another integer will always result in an integer. It may sound simple, but it is not trivial. For more information, look into linear algebra (vector spaces) and number theory. Also see https://en.wikipedia.org/wiki/Linear...#Vector_spaces