The ballroom's atmosphere crackles with surreality.
"Hacker Crackdown" by Bruce Sterling
So stark and surreal was the scene before me, that I had to remind myself that this was how the desert appeared at twilight ordinarily.
"Take Me for a Ride" by Mark E. Laxer
These are surreal, mind-boggling numbers.
"After the Rain" by Sam Vaknin
This is surreal, she thought.
"Syndrome" by Thomas Hoover
SURREAL STICKERS AND UNREAL STAMPS, William Rowe.
"Life Histories of North American Wood Warblers Part One and Part Two" by Arthur Bent
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Lottery jackpot winners from northwest Missouri say their good fortune is 'surreal'.
A Foodie With a Taste for the Surreal.
This is such a surreal picture.
A Surreal Skateboarding Journey Through China's Infamous Ghost Town.
Surreal Systems continued the more-from-less approach in the distribution of video to the home's eight TVs.
It all seemed surreal to Zach Johnson .
Manziel, Klein take in 'surreal' awards show atmosphere.
Zobrist, who plays for the Tampa Bay Rays, says when he comes home it's still a little surreal.
It was a surreal experience, even in the newsroom.
It all seemed surreal to Zach Johnson.
Hertzfeldt's 'Beautiful Day' a surreal take on mortality .
For those families who've already gone and seen the Rockettes, Mummenschanz is to provide a terrifying dose of surrealism, just in time for the holidays.
Easily the most surreal moment of my 2012 thus far was Skrillex's performance on Which Stage during Bonnaroo.
Purity Ring's 'Lofticries' Video Surreally Explores Death, Birth.
Slideshow: "Images from Alsace-Lorraine" A journey through picturesque villages to a surreal America in the heart of France.
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Perhaps one could be inspired by Conway’s theory of surreal numbers [Con94] to deal with this problem.
Global analytic geometry
An introduction to the theory of surreal numbers, volume 110 of London Mathematical Society Lecture Note Series.
The algebraic numbers definable in various exponential fields
Fields of surreal numbers and exponentiation.
The algebraic numbers definable in various exponential fields
A very brief summary of the relevant properties of the surreals is as follows. A surreal number x ∈ NO can be written in the form {XL |XR} where XL and XR are sets of surreal numbers.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
The reals are a subset of the surreals, the product of two surreal numbers is a surreal number.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
The division of two surreal numbers, say z = x/y can be constructed using z = {ZL |ZR} where ∀zL ∈ ZL : yzL < x and ∀zR ∈ ZR : yzR > x.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
The surreals are ordered in generations, and if the expression {XL |XR} allows one or more possibilities from an earlier generation then it is set to the value from the earliest generation.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
Inﬁnite sets are allowed so exp(x) is a valid surreal number.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
Deﬁne xα = exp(α ln(x)). xα is a valid surreal number because the surreal numbers are closed under exp, ln and pairwise multiplication.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
Each term of the sequence exists by closure under exp and ln, and so the limit exists as an inﬁnite surreal number.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
Lemma For surreals i q and id and lim t = P id iq, the value f 1/(lim t) is a surreal number.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
Proof The surreals are closed under pairwise addition and multiplication so lim t is a surreal. f 1/(lim t) = exp(ln(f )/ lim t) and because of closure under exp, ln and pairwise division this is a surreal number.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
Analogy denote the inﬁnite numbers by In and let all the numbers in it be constructed using lim s/ lim t Lemma lim s/ lim t is a valid surreal number.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
By this stage the reader may be thinking ”So what, surreal numbers can do everything”.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
Lemma sin(ω ) is not a separate surreal number because sin(ω ) = 0.
Banishing divergence Part 1: Infinite numbers as the limit of sequences of real numbers
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