Meaning of surreal number | Babel Free

Definitions

Any element of a field equivalent to the real numbers augmented with infinite and infinitesimal numbers (respectively larger and smaller (in absolute value) than any positive real number).

Equivalents

Examples

“Conway's construction of surreal numbers relies on the use of transfinite induction.”

“Conway's approach was to build numbers from scratch using a construction inspired by his game theory research; the resulting class of surreal numbers proved much larger than the class of real numbers.”

“• A surreal number X=(X_L,X_R) consists of two sets X_L and X_R of surreal numbers, such that no element from X_L is greater than any element from X_R. • A surreal number Y=(Y_L,Y_R) is greater than another surreal number X=(X_L,X_R), X<Y, if and only if − there is no x∈X_L such that Y<x, and − there is no y∈Y_R such that y<X.”

“Here we shall follow Conway's exposition rather closely. Let L and R be two sets of numbers. Assume that no member of L is greater than or equal to any member of R. Then #92;#123;L#92;vertR#92;#125; is a surreal number. All surreal numbers are constructed in this fashion.”

CEFR level