Smallest Element is Infimum/Examples/Arbitrary Example 2

Example of Use of Smallest Element is Infimum

Let $T$ be the subset of the set of real numbers $\R$ defined as:

$T := \set {x \in \R: 1 \le x < 2}$

$T$ has a smallest element $1$.

Hence from Smallest Element is Infimum it follows that $1$ is also the infimum of $T$.


Sources

  • 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 2$: Continuum Property: $\S 2.8$: Example $\text{(ii)}$
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