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The term that refers to events occurring without any connection to each other is "discrete." In various fields, such as mathematics and statistics, "discrete" specifically describes distinct or separate values that do not form a continuous sequence. In this context, discrete events are those that do not influence or relate to one another; they stand alone without any overlap or interaction.

The choice "discreet," while similar in pronunciation, pertains to being tactful or careful in one's actions or speech, which is unrelated to the concept of events being separate. The terms "incident" and "incidence" also diverge from the correct definition. An "incident" typically implies a specific occurrence or event, often with a negative connotation (such as an accident), while "incidence" refers to the frequency or rate at which something happens, particularly in epidemiology. Thus, "discrete" is the appropriate term for describing independent, non-connected events.