Where something exists there is space. This space is not lost but filled with form: the limiting factor of possibility. A vacuum has infinite potential in terms of what it attracts.

Adding to space
Mathematics is an understanding, of the relationship of concepts. The language and syntax are developed as tools to aid the understanding of those who do not have an innate experience of the depth of feeling of infinite space.

The intellectual process of investigation is linear in that one discovery leads to another and the development of the language clarifies the process of mental rigours.

Whereas I may not know, innately the answer to an apparent question, the answer always exist and there really is no question. The question is just one way of finding a concept, a concept that may come intuitively for another.

The first well documented foray into maths is the understanding of natural numbers, that is those used for counting: from one to infinity. There is no zero in counting and, in theory, no upper limit; one can be added to any number no matter how large. In fact any number can be added to any number and the result will be another natural numbers. This set of numbers is noted by a capital N and every whole number from one to infinity is an element of N {1,2,3 e N} or {a,b,c... e N}

The natural number line:
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23, . . . }

Addition is the process of whereby starting in the number line with one of the numbers to be summed the other is counted along the line, the last being the sum of the two numbers

4+11
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23, . . . }

11+4
{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19, 20,21,22,23, . . . }

It should also be noted that numbers to be added can be added in any order with the same result; i.e. {1+2}={2+1}. This quality of addition is called commutivity: Addition is commutative

The quality of having the addition any two natural numbers resulting in another natural number is 'closed'.

So addition is {closed and commutative}