Like for example (1, 9)
The maximum would be 8, because we are talking about natural numbers, so the problem of an undefined maximum (the number right before 9) doesn't exist?
Am I right?
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The maximum would be 8, because we are talking about natural numbers, so the problem of an undefined maximum (the number right before 9) doesn't exist?
Am I right?
$(1,9)$ is by definition the set of real numbers both greater than $1$ and less than $9$. Using $(1,9)$ to mean something else will only cause confusion to you and others, and so there is no point in doing so unless the purpose is to cause confusion.
If you want to talk about the set of integers greater than $1$ and less than $9$, then you could write: $\{ x:\ x\in (1,9), x\in\mathbb{N} \}\ $ or $(1,9) \cap \mathbb{N},\ $ or $(1,9) \cap \mathbb{Z},\ $ but the most standard way to write this set is just to write the list itself: $\{ 2,3,4,5,6,7,8\}.$