  Surreal numbers form the ultimate extension of the field of real numbers with
infinitely large and small quantities and in particular with all ordinal
numbers. Hyperseries can be regarded as the ultimate formal device for
representing regular growth rates at infinity. In this paper, we show that any
surreal number can naturally be regarded as the value of a hyperseries at the
first infinite ordinal $\omega$. This yields a remarkable correspondence
between two types of infinities: numbers and growth rates.
