R^ω (pronounced "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^ω, however, is an infinite-dimensional space even larger than R^∞ ("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^ω is just like R^∞ in the sense that its tuples are infinite sequences of real numbers. But while every infinite tuple in R^∞ must eventually end with an infinite string of zeros, each of the infinite ordinates in an R^ω 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^∞ if an infinite string of zeros is annexed to each n-tuple. What this means, then, is R^∞ is actually contained inside the much larger R^ω.