: Can fiction be written without a coincidence? Does every fiction has a coincidence? Is there any evidence for a fiction not having a coincidental occurring at all ? I understand by the time

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Of course fiction could be written without coincidence. Things can follow a linear path and reach their foregone conclusion, as they do sometimes in real life.

However, coincidence is not a "binary" category - things have some (possibly unknown) probability of happening. If a story hinged on the possibility of someone walking in on a private conversation of some characters, it would be less of a coincidence than relying on a coin landing on it's edge and remaining so. But also the former is coincidence - just more likely than the latter.

So writing without any coincidence in the extreme sense is probably very difficult. Therefore, the real question should not be whether it could be written this way, the question (as with every literary device) is what purpose does coincidence serve in the story, specifically coincidence that is emphasized as such. You can then decide you don't want to achieve that purpose in your writing, or to achieve it with other means.

To answer this, I think there are two major things coincidence achieves in fiction:

Allowing interesting and surprising plot twists, especially in critical points in the story. The fact that many things COULD happen, but a specific one DID happen, allows you to choose the one that serves the story most. When escaping enemies, the heros could find an undetectable alley that allows them to escape quietly, or they might not notice the alley and have to run in broad daylight in the market square, leading to an exciting chase. Choose the one that is more interesting to you.
Adding a sense of wonder and excitement. Coincidence comes many times bound together, paradoxically, with a sense of fate/destiny/prophecy [in fantasy. In a 007-novel it would be the hidden hand of MI5, for example]. The reason for this is that when you have a known fate for a character, then reality has to somehow arrange itself around this fate, which leads to coincidences to happen. In this way, coincidence is really not coincidence - it's intelligent design in the guise of coincidence, which generates a sense of mystery and wonder.

The last point I'd like to make is how much coincidence is allowed. Here, I'd like to paraphrase "Sanderson's First Law of Magics", which states that: "An author's ability to solve conflict with magic is DIRECTLY PROPORTIONAL to how well the reader understands said magic". Similarly, I'd suggest that the more unlikely the coincidence, the less should it be relied on to solve problems in the story. For example,

If you want the evil genius to die of a heart-attack right before he
presses the big red button that will destroy the world, he better be
an 80-year-old with a heart condition, not a 33-year-old in top
condition.
However, if the 33-year-old in top condition is just the
hero's butler, and you use his sudden death to bring a new butler to
the mansion, it does not matter how coincidental his death is. Kill him with
a simple accident or a shocking heart-attack - the reader won't care, since
the coincidence is not critical to the story.

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Of course, it can.

Coincident is generally defined as occurring together in space or time.

It does not mean that there is no explanation why some events occur simultaneously. There always is. The personal preferences of writers vary when it comes to revealing the

Consequences--results or effects of actions or conditions.

to the readers, but it is a matter of style, genre, how high you are suspending the disbelief and what not.

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Absolutely so.

Some best detective and strategy (Chessmaster trope warning! TV Tropes link!) novels have absolutely zero coincidence. They are duels of wits, a game with firm rules and moves chosen as optimal. Contingencies, backup plans, backups of backup plans, foreseeing the next move of the opponent or even manipulating them into making it - a perfectly deterministic setup with zero randomness.

With best detective novels you are getting at first the complete set of clues and rules of the game, and then playing it optimally you can reach the conclusion and authoritatively guess the "murderer" less than halfway into the book. The other half gradually uncovers additional clues, which make the task increasingly easier, until you reach the conclusion - the solution of the puzzle, where our protagonist uncovers the guilty.

In these genres coincidence is a cheap lockpick, a joker card used whenever the author is unable or unwilling to design a fully deterministic reason. It can always be used to explain certain events or finds - but every such use reduces the value of the novel, because instead of rigid rules to be followed in logical reasoning, we have a bit of chaos, something the reader is unable to foresee, and therefore "unfair" in the game which the novel is.

Now, if instead of that, you're writing romance, adventure, horror - you're free to use coincidence. The reader is not expected to foresee the future, neither given enough clues nor able to embrace the nebulous, always-changing rules. It's not a puzzle, it's a ride. Of course you're still able to include "mystery puzzle" elements, be it as short episodes / side threads, or as the central core surrounded by decoration of chaotic fantasy flair. It's an extra flavor, an extra challenge to the reader, and as such, the isolated part should follow the "no coincidence" rules of the game.

But never forget Rule of Cool warning! TV Tropes link!. In short: you don't need much explanation, much exposition or generally going to great lengths with your coincidence if its effects are awesome.

If you compare your painstakingly, precisely built mystery to a house of cards, placing the last card on top of the house of cards is quite satisfying, but crashing a transatlantic cruise ship into it might be more entertaining.

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coincidence: a striking occurrence of two or more events at one time apparently by mere chance (according to WordReference.com)

For me, the key idea behind coincidence is the fact that it is striking. That two people happen to be in the same busy café and end up sharing a table, thus leading to a nice conversation and friendship, is not coincidental. That these two people turn out to have been colleagues in the first year of primary school is a coincidence. That they turn out to be estranged mother and daughter who hadn't seen eachother in over twenty years is a huge coincidence.

I believe the problem with coincidences in fiction is twofold:

all it takes is one huge coincidence (poorly handled) to make the story feel forced (personally, I get really annoyed with these ones) *
accumulation of small coincidences that would blow over unnoticed if used in fewer numbers

But your question is not about what constitutes fair use of coincidences.

Can you write a story without a single one? I should think it's perfectly possible. I don't usually count how many coincidences I come across in stories I read (and a well-used small coincidence can very well go unnoticed until you start looking for them), but it's not impossible to do so.

Do notice that some genres may rely more on coincidences than others: romance, I believe, is one such because a good coincidence can bring in surprise and up the tension. Then there is mystery, where a reader may even doubt if the coincidence was in fact so, or a carefully crafted event.

Just to stress this idea, a huge coincidence can make a great novel. The Portuguese writer Eça de Queirós wrote his famous Os Maias using a huge, jarring coincidence, yet did it so well it came off almost as a natural event, something even likely to occur.

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