# Category:Continuum Property

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This category contains pages concerning **Continuum Property**:

The **continuum property (of the set of real numbers $\R$)** is a complementary pair of theorems whose subject is the real number line:

### Least Upper Bound Property

Let $S \subset \R$ be a non-empty subset of the set of real numbers such that $S$ is bounded above.

Then $S$ admits a supremum in $\R$.

This is known as the **least upper bound property** of the real numbers.

### Greatest Lower Bound Property

Let $S \subset \R$ be a non-empty subset of the set of real numbers such that $S$ is bounded below.

Then $S$ admits an infimum in $\R$.

This is known as the **greatest lower bound property** of the real numbers.

## Pages in category "Continuum Property"

The following 10 pages are in this category, out of 10 total.