Visualizing mathematical structures is a broad and important subject in mathemat- ics education. Consider, for example, the difficulty of seeing a number system that includes infinitesimals. This might seem an obvious observation since infinitesimals are infinitely small, but that is not the point I wish to make here. In mathematics we have tools that allow us to think visually about objects far beyond direct physical perception. We can see the infinite. We use our natural intuition of the geometiy of three dimensional space as a starting point for constructions of abstract mathematical structures, such as higher dimensional vector spaces, non- euclidean geometries, and topological spaces of various kinds. Those structures often do not seem to have direct interpretations in the physical universe we know, but nevertheless we can picture them in the mind's eye. With simple images we can illustrate, quite accurately, more abstract concepts. Precision and formal rigor are essential in mathematics, but these qualities apply only to the final products of mathematical activity. When we domathemat- ics, we rarely think formally. We do not limit ourselves to computations and rigorous proofs. Rather, mathematicians work with pictures visual representa- tions of mathematical structures. The same pictures also seem indispensable in learning mathematics. Some mathematical structures, however, cannot be visual- ized easily. A level of abstraction and set theoretic methods are necessary to prove that certain structures even exist. A theorem of Stanley Tennenbaum's (5), pub- lished in 1959, states that certain mathematical structures are very complex. The notion of complexitz7, as used in Tennenbaum's theorem, has precise meaning, and I will say more about it later. At this point let me just mention that the theorem excludes the possibility of a simple presentation of some structures, and the number system of nonstandard analysis is one of them. Nonstandard analysis was created (or perhaps recreated) by Abraham Robinson (4), who reintroduced infinitesimals to mathematics using the formal apparatus of mathematical logic. Since then, much has been written on the theory of infinitesi- mals and their applications. Part of the effort was directed towards utilizing some of the new methods and techniques in teaching. Nonstandard analysis offers great simplicity in defining basic concepts. Think, for example, of the following defini- tion of the derivative: y = f(x) is differentiable at a point a, and b is the derivative of f(x) at a, if for every number dx infinitesimally close to 0, dy ff a + dsc) - f( a)