We have to be careful here. It is very hard in practice to distinguish numbers from the symbols used for their representation.
And the very nature of such representation is that we thereby give a distinct phenomenal identity to number (as represented by its symbol).
So when I use the symbol "1" to represent the notion of one, it thereby assumes this phenomenal identity.
Furthermore because understanding of number in our culture is dominated by its quantitative aspect, numbers thereby become misleadingly identified as abstract phenomenal objects (with an absolute identity).
However in truth the meaning of number is much more elusive.
As I have been at pains to illustrate, every number has both a qualitative as well as recognised quantitative aspect. Basically, the quantitative aspect relates to the notion of number as independent (i.e. where phenomenal poles such as external and internal are separated). The corresponding qualitative aspect relates to the corresponding notion of number as interdependent (where these same poles are understood as inherently complementary and ultimately identical).
We can easily illustrate this with respect to 1.
In conventional terms 1 is given a mere quantitative meaning i.e. as a separate number object. This notion is indeed extremely important and serves as the fundamental basis for discrimination of any phenomenal object. Therefore in order to recognise an object phenomenon as a distinctive unit, the quantitative notion of 1 must necessarily be already implicit in such understanding.
However 1 can equally be given a qualitative holistic meaning as "oneness". The best example of this relates to the ultimate experience of spiritual oneness (where the explicit notion of an object as a separate phenomenon no longer arises).
So the very notion of 1 in this alternative qualitative sense pertains to the notion of pure interdependent relatedness (based on the identity of opposite poles).
Put another way, the quantitative notion of number is based on either/or linear logic, where the positive poles excludes the negative..
Therefore in the expression where 1 - 1 = 0, 1 ≠ 0.
However the qualitative notion of number is based by contrast on both/and circular logic, where the positive pole includes the negative.
Therefore from this perspective where 1 - 1 = 0, 1 (as oneness now defined in this complementary manner) = 0 (as nothingness).
However before we can understand the (common) interdependence of opposite poles, we must recognise their (separate) independence (and vice versa).
So properly understood, both the quantitative and qualitative notions of number are inextricably linked in all experience.
Thus, the ultimate notion of number (though necessarily implicit in all phenomenal observation) is of an ineffable nature where both quantitative and qualitative aspects coincide.
In this sense, though we must necessarily represent numbers in phenomenal terms with symbols, they cannot be confused with physical phenomena (where number is already inherent in their recognition).
Put another way, physical phenomena themselves represent a certain rigid confusion with respect to the quantitative and qualitative aspects of number. In other words, we can only recognise such phenomena, through maintaining a certain imbalance with respect to the quantitative and qualitative aspects of number.
Once we recognise a physical object for example, we thereby associate number with its merely quantitative aspect.
In this sense the very quest for ultimate spiritual unity is the corresponding desire to reconcile both the quantitative and qualitative aspects of number in their original ineffable state.
So 1, in the unity of all form (through circular understanding) as pure interdependence is inseparable from 0 (as the emptiness or nothingness with respect to separate phenomena).
Thus once again, 1 - 1 = 0.
However when we switch to linear (quantitative) logic, both poles are now positive
So we have 1 + 1 = 2.
Thus duality (as the qualitative meaning of 2) arises from application of the alternative logic.
In dynamic terms, all phenomenal reality in its forms and transformations represents the dynamic interaction of both types of logic (representing the quantitative and qualitative aspects of number).
So from this perspective, we could say that the very goal of all evolution is to ultimately realise the true original state of number (where quantitative and qualitative aspects are indistinguishable).
And all the fundamental mathematical operations can be validly seen as an extension as to what is implied through the notion of number.
This thereby gives an extraordinary significance to the role of a more comprehensive mathematical understanding (where both its quantitative and qualitative aspects are explicitly recognised).