Imaginary Number Space

Zero Sail.jpg|'Zero Sail' dive through Imaginary Number Space by the Shadow Border
Imaginary Sea.png|Imaginary Number Space Sea
Myuverse Shirou stabbing Miyuverse Sakura.png|Shirou and Sakura falling into the Imaginary Number Space.
 is an alternative space within the Reverse Side of the World from which the Magecraft concept of Imaginary Numbers originates, separate from Real Number Space that constitutes the primary reality of the universe.Fate/Grand Order: Cosmos in the Lostbelt - Second Prologue - Section 8: On to an Unprecedented Journey
==Characteristics==
The Imaginary Numbers Space is the inner side of the world, an unobservable territory, undetectable by the current laws of physics. It contains all possibilities due to being unobserved, though for that same reason nothing actually exists within it, so things like landmasses should be impossible. If one were to use Imaginary Dive Technology to view it, all they would see are rainbows; however, the rainbows are just illusions made observable by the Dive technology, and each person would see the rainbows differently.Fate/Grand Order: Cosmos in the Lostbelt - Imaginary Scramble: Great Void Sea Battle - Section 1: The Unknowable Reef
It is not normally hostile to normal reality, which are known as "Real Numbers", but if the Imaginary Numbers were made observable and thus everyone sees the same rainbows, then they could become lethal to normal life and the interaction between Real Numbers and Imaginary Numbers becoming observable to each other can cause insanity. 
It is possible to construct a special Mystic Code with a memory chip branded with an Imaginary Numbers Magecraft formula that would allow a person's awareness to be considered normal in Imaginary Numbers Space, however it only works for Servants with special Spiritron Dress or Spirit Origins. Although one with such a Mystic Code could interact with Imaginary Numbers, should the nature of Imaginary Numbers be altered to allow for living things to exist in the Imaginary Number Space where it would normally be impossible, then said monsters would be unable to be seen through sight and light, and instead methods using heat and sound must be employed.
The Far Side of the Moon is an instance of Imaginary Number Space,
 and BB is capable of utilizing Imaginary Number Space.
Fate/Grand Order - BB (Swimsuit), Profile Passionlip's Breast Valley is an imaginary number space pocket.
 Kingprotea was originally sealed by BB at the ends of the imaginary number space, as BB realized she was too dangerous to be left unattended.
Fate/Grand Order material VIII - Kingprotea's profile translated by King of Padoru
===Traversal===
It is possible to travel through Imaginary Number Space in specialized craft such as the Imaginary Numbers Submersible Shadow Border, with the use of the Imaginary Numbers Observation Device Paper Moon, though the method is difficult and inherently dangerous.Fate/Grand Order: Cosmos in the Lostbelt - Anastasia: Permafrost Empire - Prologue In performing a 'Zero Sail' dive in this way, the craft departs from normal reality and dives into the 'sea' of Imaginary Numbers, and requires a connection or bond to be formed to an existence within the normal reality in order to surface.
Imaginary Number Space has 'tides' which can cause a time difference between vessels passing through it and normal reality.
===Imaginary Trench===
In the Imaginary Scramble event, the Outer God known as the Evil God of the Flowers planned to use the Imaginary Number Space as a base to invade real Earth. To achieve this, using its association with sleeps and dreams, it placed the crew of the Nautilus into a dream that it could make the contents of "real", which is where the event takes place.
It summoned Van Gogh as a Foreigner into the space, who in turn would call Katsushika Hokusai. Using Van Gogh's Noble Phantasm to modify Hokusai's Saint Graph using Skill alteration in order to increase the interaction and influence her respective Outer God has over her, Hokusai would use their Noble Phantasm to turn the Imaginary Space into an Imaginary Sea, making it observable for its purposes of gathering eldritch energy from feeding on fears and madness brought on by the interaction between Imaginary and Real Numbers from Nautilus' crew. 
Meanwhile, Van Gogh would be used to turn the sea into landmasses and to make a base, forming the Imaginary Trench, with an automatic Magecraft formula within Gogh's blood being uses as a catalyst to spawn monsters to fill the sea, like the Enemy Ship. Once enough eldritch energy was collected, Van Gogh would use her Noble Phantasm to deify the Foreigners, allowing for the Outer Gods' complete advent into their true form using the eldritch energy and put them in a position to invade Earth, even if it takes millennia afterwards.
==History==
===Fate/stay night===
Sakura Matou can access pockets of Imaginary Number Space to store objects and even people. In the Heaven's Feel movie adaptation the Shadow uses Imaginary Numbers to absorb a fireball from Caster. When Gilgamesh confronts Sakura she uses Imaginary Numbers portals to redirect his attacks from Gate of Babylon. It is also presumably where blackened Berserker and Saber Alter reside when they are not actively fighting.
In the Femme Fatale bad ending, Sakura traps Rin Tohsaka and Shirou Emiya inside Imaginary Number Space.
===Fate/EXTRA CCC===
After Tamamo-no-Mae was forced to regrow her tails in order to save Hakuno Kishinami from the Moon Cell, she severed them and sealed them in Imaginary Number Space. However they attained sentience, becoming the Tamamo Nine, and managed to escape.Fate/EXTRA CCC - Tamamo Ending
BB made use of Imaginary Number Space during the C.C.C. incident.Fate/EXTRA CCC
===Fate/Grand Order===
Ars Paulina, Solomon's The Grand Temple of Time, which later came into the possession of Goetia, is located in the Imaginary Number Space.Fate/Grand Order - Salomon: The Grand Time Temple - Section 11: Throne of the Light Band Tiamat was previously sealed within the world of Imaginary Numbers.
Following the destruction of Chaldea Security Organization at the hands of invaders from the Lostbelts, the survivors were forced to dive into Imaginary Number Space in the Shadow Border to escape the Oprichniki overwhelming the Antarctic coastline. After a week in Imaginary Number Space, they formed a connection to their attackers and managed to resurface in the Russian Lostbelt, with three months having passed for the planet.
The Shadow Border performed another short dive to enter the Norse Lostbelt, during which there were signs of something else nearby within Imaginary Number Space.Fate/Grand Order: Cosmos in the Lostbelt - Götterdämmerung: Eternal Ice-Flame Century - Prologue This "something else" was later revealed to be Nemo aboard his Nautilus submarine.Fate/Grand Order: Cosmos in the Lostbelt - Yuga Kshetra: Genesis Destruction Cycle - Section 19: Final Dark God Nemo and his Master Sion Eltnam Sokaris would go on to join the crew of the Shadow Border, using the Nautilus to aid them in traveling through Imaginary Number Space.
The Storm Border has at least six Virtual Triton Engines which can draw power from Imaginary Number Space to power certain armaments.Fate/Grand Order: Cosmos in the Lostbelt - Nahui Mictlan: Golden Sea of Trees Travelogue - Section 1: To the Land of the Dead
===Lord El-Melloi II Case Files===
Trisha portal.jpg|Trisha Fellows opening a pocket to the Imaginary Number Space.
Trisha in Imaginary Space.jpg|Trisha Fellows's decapitated head in Imaginary Number Space.
Trisha Fellows uses Imaginary Numbers Magecraft, and when she was decapitated she created an Imaginary Number Space pocket for her head to fall into so that Doctor Heartless would not be able to get her Mystic Eyes. Olga Marie Animusphere later discovered the sealed pocket dimension and was able to open it using a password that Trisha had set ahead of time. Due to the nature of the Imaginary Number Space, her head is still alive as anything within the space is unaffected by space and time, allowing her the brief chance to tell the people who find her head as to who killed her before she dies.Lord El-Melloi II Case Files Volume 5: case. Mystic Eyes collection train (Lower) - Chapter 2 Part 1
==References==
vi:Không Gian Số Ảo
Category:Locations
Category:Cosmology
Category:Terminology in Fate/Grand Order
Category:Terminology in Lord El-Melloi II
Category:Terminology in Fate/EX
Category:Terminology in Fate/stay night
Category:Terminology in Fate/kaleid liner PRISMA☆ILLYA
Category:Sakura Matou (topic)