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## 7969Definition: Incidence

By incidence, we mean in projective geometry that a point and a straight line, or a point and a plane, or a straight line and a plane are subsets and supersets of each other in the set-theoretic sense. In other words, if $A$ is a point, $l$ is a straight line and $\alpha$ is a plane, then

• $A$ and $l$ are incident (or “$A$ lies on $l$”, or “$l$ passes through $A$”), if and only if $A\subset l,$
• $A$ and $\alpha$ are incident (or “$A$ lies on $\alpha$”, or “$\alpha$ passes through $A$”), if and only if $A\subset \alpha,$
• $l$ and $\alpha$ are incident (or “$l$ lies on $\alpha$”, or “$\alpha$ passes through $l$”), if and only if $l\subset \alpha.$

| | | | | Contributors: bookofproofs

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