Coincidence is the feminine noun that means the coincidence, indicating events that occur simultaneously. It is synonymous with coexistence, agreement and simultaneity.
The word incidence means occurrence or event, while the prefix "co" refers to the concomitance or simultaneity of two elements.
In some situations the word coincidence can mean chance, because it describes a situation that occurs without prior arrangement. In these cases, mere coincidence can be one mere chance. Ex: I didn't know she was going to be at that party, we met by coincidence.
Many people claim that there are no coincidences and that everything is foreseen by God or fate.
The word coincidence can also refer to the confluence of attitudes or opinions, when some kind of agreement is reached. Ex: The war was avoided because the leaders' opinions coincided at the very first meeting.
In the context of fictional works such as movies or books, it is normal to verify the phrase "any similarity is mere coincidence". This means that even if some fact or character revealed in the work is very similar to real life elements, this is the result of chance and was not done deliberately. It is a phrase used to avoid possible lawsuits.
Regarding the correct form of writing, many people have doubts between coincidence and knowledge. However, the correct form is coincidence, because knowledge is a word that is not part of the dictionary.
In the area of Geometry, there is coincidence when two geometric figures are superimposed.