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In Lucian's True Story the people of the Moon are at war with the people of the Sun. The narrator not only survives going to the sun, he doesn't seem impressed by it at all. Of course every word of the story is like that the operates on logic such as "Aristophanes is a wise and truthful man".
Nora and Maya from Crushed look so good in their swimsuits they can make Nigel, a blind man, have a Nose Bleed.
Later novels in more or less follow the line that a witch's curse works if and only if the target knows they've done it. Unlucky Charlie, the target for the cursing at the Witch Trials, cannot be aware they've done it because he's a scarecrow, so points are given for general inventiveness. Except for the year when Granny Weatherwax made his head explode.
Going Postal deconstructs the trope. Moist knows its impossible for the postal service to beat the clacks in a long distance race so instead of trying to beat the laws of physics he works with them to win the race. he implants a Engineered Public Confession into the Clacks' message that gets Glit arrested.
From the same book Vimes manages to survive hosting the Summoning Dark. While he isn't the first to do so (though those that have are far and few between), the fact that he suppressed the berserker rage it causes is stated by the everyone who knows about Dwarf curses to be impossible.
Ronnie Soak from Thief of Time somehow managed to milk an alligator.
The Lord of the Rings: Tolkien took a stab at implying Eldritch Abominations by having Gandalf speak of unexplained creatures that were older than Sauron himself. However, creation myth in The Silmarillion indicates that at first only Eru existed, and then, while the world still did not exist, he created the Ainur... of which Sauron is one. So, while not implying this is how Tolkien thought of it, anything being older than Sauron is indeed pretty mind-bendingly Lovecraftian, since they seem to have no possible place in Creation.
In Xanth the talent of being immune to magical harm is theorized to be capable of this. The talent includes indirect magical harm in its protections so something like magically hiding the edge of a cliff from him and trying to get him to fall off wouldn't work either. This is where the trope comes in. It's theorized in-universe that when the omnipotent demon that's the source of all magic in Xanth left, shutting all the magic down, it came back very shortly afterward solely because of this talent, as putting him in danger by removing magic could be considered indirect magical harm. That's right, it's so powerful that it can even affect its own omnipotent source.
Journey to the West. To destroy Sun Wukong the Celestial Heavens create a fire that is specifically supposed to kill immortals like him. Even after weeks inside it he's still alive. The gods turn to the Buddha who resorts to Sealed Badass in a Can.
His Dark Materials devotes a scene to demonstrating how Panserbjørne cannot be lied to, tricked, bluffed, or otherwise deceived in any way. Lyra does just this to the king of the Panserbjørne. When Iorek hears this he gives her the title "Silver-tongue".
Iron Druid Chronicles justifies the trope. A big part of why Atticus is so powerful is because he experiments with the rules of druid magic and was able to find solutions to problems that seemed Impossible to the much older and powerful Tuatha Dé Danann.
In book 1, the fairies state repeatedly that escaping a time stop is impossible because they are sure that it is physically impossible to do so. Artemis uses Loophole Abuse to find a way to do it: since the time stop prevents anyone from changing their state of conscious naturally he theorized that by artificially forcing a change he could slip through.
For thousands of years, the fairies have had to deal with a seemingly absolute curse that takes away their magic if they enter a human dwelling without permission. This is a major plot device in the first few books. Then No1 the Teen Genius warlock shows up. He lifts the curse effortlessly.
In the Molly Moon series, Molly has a book that teaches her the rules of hypnotism. During the bank heist, she hypnotises an iris scanner.
Mmmeee0 once converted all the adrenaline in his Body into THC. Adrenaline is a Hormone and THC is only produced in Plants. From a Chemical standpoint, the two are nothing alike. The Creepy Teen Years
Nynaeve's main passion is Healing, up to and including inventing her own spells for it.: One of them heals severing.
When Mat escapes from the Tower of Ghenjei, Olver wins a game of the Unwinnable Joke Game Snakes and Foxes without cheating, utterly confusing Talmanes.
Warrior Cats Despite Scourge when he rips out ALL NINE OF TIGERSTAR'S LIVES AT ONCE. A cat is supposed to be temporarilly dead once killed only to revive later. To take out all nine at once is unprecedented.
In the Honor Harrington books the theta band of hyperspace has been an unsurpassable speed barrier for centuries. Then the Mesan Alignment invented the streak drive that can not only exceed it, but exceed it by two levels.
In book 34 of Animorphs Cassie morphs to whale, while still demorphing from osprey. Every time someone does a rapid switch from one morph to another, they have to revert fully to humans before they can start morphing agin.
Burying the Shadow: No soulscaper has ever healed an eloim. Ultimately in order to heal the eloim, Rayojini has to die and pass into Elenoen. She not only succeeds, she's brought back to life.
Gotrek & Felix start as relatively typical heroes of the setting but by the end of the third book they've done things that should by all accounts never happen by the rules.
Good Omens: a car that has run without gas for decades and a stereo system that works without speakers are just two of the countless instances of Crowley getting objects to work for him against all logic and physical possibility.
Dark Heavens: When Xuan Wu is asked to make a sphere of water as cold as he can, he has to severely limit himself to avoid destroying the world by lowering the temperature to Absolute Zero. "Absolute Zero" is a theoretical temperature that's supposedly impossible to reach and yet he has to hold himself back from it.
Mistborn Vin can pierce copperclouds, something which the laws of Allomancy and all of Kelsier's crew state is impossible. The Hero of Ages reveals that she's actually using Hemalurgy to enhance her abilities as a Seeker.
At the end of the first book, she also 1) pulled metal from another person's body, which is impossible based on the laws of Allomancy 2) used Allomancy without any metals, which is what the power comes from and 3) used the mists to power her Allomancy, which no one had ever done before.
Fergards Souls: Melchior "Midnight" Herald was placed in The Abyss, a giant graveyard for everything that could possibly breathe and exist in this world. He simply left it after one year. Both angels and demons with an exception of Samael state this is literally impossible to do.
The Ugly Barnacle: Can anything be ugly enough that it kills everyone? Yes, yes it can.
Sword Art Online: A really big moment when a character takes a killing blow from Kayaba Akihiko to save Kirito, while paralyzed. Even Kayaba couldn't believe that happened, and he made the game.
The Stainless Steel Rat provides 400 proof alcohol. "Proof" is a system of identifying the percentage of alcohol in a liquid. The formula for determining the proof of an alcoholic mixture is [1.750*ABV] (where ABV is the Alcohol By Volume). This means the proof of such a mixture is close enough to "double the percentage of alcohol" in it that that's what most people think it is. 400 proof alcohol would be 229% alcohol by volume.
The Hexslinger Series: Ixchel creates a way for hexes to live and work together without wanting to devour each other's power and life, breaking one of the only known absolute rules of magic.
The Pendragon Adventure: In the climax of the last book Saint Dane dies because his followers turn on him without any acknowledgment that this doesn't follow from the rules laid down only a few hundred pages ago.
Star Wars The Expanded Universe: Mandalorian battle armor zigzags this trope Depending on the Writer. Cannoically there are only three materials that can resist light sabers: cortosis, phrik and beskar. Everything else gives no resistance. The Mandalorian smiths have exclusive knowledge of the last of those and so the armor they made can be impervious to light sabers, but sometimes it's as useless as the Storm Trooper armor.
Ra: There's an entire chapter called The Seventh Impossible Thing. Magic is poorly understood even by cutting-edge researchers, so a lot of things that are believed to be impossible at some point (starting with the existence of magic itself) turn out to be very possible indeed.
In Game of Thrones, Bran enters Hodor's mind, something that Jojen says no one else can do.
While wargs are common beyond the Wall, and there are even some further south, Bran is the first person in history to be able to warg into another human.
According to Melisandre, bringing Beric back six times should be impossible, even for a Red Priest.
In Codex Alera, specific circumstances make it become this trope. Watercrafters can heal injuries, though having the injured immersed in a tub of water makes it much, much easier. Only the High Lords and Ladies and the First Lord can heal life-threatening injuries without a tub. Unless you're Isana, whose watercrafting skills equal or possibly exceed their talents even though she isn't even a Citizen.
Log Horizon: A justified case. "World Class Magic" is described as "magic that changes the laws of the world". In other words, one of the laws governing this setting allows for the changing of other laws. Shiro's contract that transforms landers into adventurers is described as this kind of magic.
Warcraft: One of the novels reveals that after the War of the Ancients, Deathwing tried mating with his consorts; his deformed, fiery body was so hot he burned three of them to death and horrifically scarred the fourth. For reference, black dragons are immune to fire and regularly take baths in molten lava.