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## Definition: Points, Straight Lines, and Planes

Let $\mathcal P$ be an arbitrary non-empty set. The elements $A,B,C\ldots \in \mathcal P$ are called points.

Let $\mathcal L$ be an arbitrary non-empty set. We call the elements $a,b,c \ldots \in \mathcal L$ lines.

Let $\Pi$ be an arbitrary non-empty set. We call the elements $\alpha,\beta,\gamma \ldots \in \Pi$ planes.

### Notes

• Points $\mathcal P$ constitute the elements of linear geometry.
• Points $\mathcal P$ and straight lines $\mathcal L$ constitute the elements of plane geometry.
• Points $\mathcal P$, straight lines $\mathcal L$, and planes $\Pi$ constitute the elements of spacial geometry.

| | | | | created: 2019-12-21 05:28:01 | modified: 2019-12-21 06:35:34 | by: bookofproofs | references: [6260], [8231], [8251], [8324]

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