R-Omega is an infinite-dimensional space residing at the boundaries of our intellect. We first learn of R2 in middle school (two-dimensional space), and our physical universe can be described in terms of R4 (four-dimensional spacetime). R-Omega, however, is an infinite-dimensional space even larger than R-Infinity.

Any point in any space can be described by a sequence of real numbers called a tuple, each number being an ordinate (points in R2 are described by 2-tuples, nicknamed coordinates). R-Omega is just like R-Infinity in the sense that its tuples are infinite sequences of real numbers. But while every infinite tuple in R-Omega must eventually end with an infinite string of zeros, each of the infinite ordinates in an R-Omega tuple is free to be any real number.

One can think of R2 as being contained inside R3 if a zero ordinate is annexed to each coordinate in R2 (geometrically, we can envision the two-dimensional Euclidean plane of R2 resting inside the three-dimensional space of R3). Similarly, every n-dimensional space Rn is contained within R-Infinity if an infinite string of zeros is annexed to each n-tuple. What this means, then, is R-Infinity is actually contained inside the much larger R-Omega.