In this paper we formally construct (mathbb{M}), a number system that contains three dimensions and forms a bridge between the complex numbers and the quaternions. In this system we define the operation of division by zero (1/0=infty). The third dimension of the system is the scalar infinity (s), which does not mix with real or complex numbers.Historically, a system with exactly three dimensions was impossible because of the multiplication of two new axes. In the quaternions these are (i) and (j), whose product must give (k), creating a new dimension because (ij) cannot be displayed in those three dimensions. Historically, taking the square root of (-1) was not allowed. This was solved by the new number (i), which introduced the complex numbers and achieved the transition from (mathbb{R}) to (mathbb{C}) by adding the new number (i) such that (i^2 = -1). (mathbb{R}) is one-dimensional, and (mathbb{C}) is a two-dimensional number system, so the question arises whether there are number systems above (mathbb{C}).The answer was first found by William Rowan Hamilton when he tried to construct a three-dimensional number system. By adding one new axis (j) such that (j^2 = i^2 = -1), he encountered the problem of what the product of (i) and (j) would give. He realized that it would give (k), a new spatial axis, and so he constructed a four-dimensional number system with axes (1,i,j,k) such that (k^2 = j^2 = i^2 = -1). Thus the three-dimensional algebra was skipped because no matter which axis we add, the product of two axes must always give something new, namely a fourth dimension.Later Frobenius and Hurwitz formalized this and proved that number systems are possible only in dimensions (2^n), where (n) is a natural number: namely 1 ((mathbb{R})), 2 ((mathbb{C})), 4 ((mathbb{H})), 8 ((mathbb{O})), and so on, up to 256 dimensions and beyond. This is the Cayley-Dickson construction, and the number systems obtained after the sedenions are no longer particularly interesting or useful for study because they lose critical properties such as associativity, alternativity, and commutativity.All these systems do not solve the problems for which new systems are introduced, namely the definition of undefined numbers. Just as the complex numbers define the square root of (-1), which was undefined in the real numbers, so the definition of (n/0) brings with it the definitions of other undefined numbers, such as the zeroth root and zero to the zeroth power.