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.