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Is this true

$\dfrac{-1}{n}< 0 $ for all n$\in \mathbb{N}$?

Or is it false and I have to write:

$\dfrac{-1}{n}\leq 0$ for all n$\in \mathbb{N}$

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    The meaningfulness of these statements depend on whether $0 \in \mathbb{N}$ but most mathematicians would agree that $\infty \not \in \mathbb{N}$.2011-09-25

1 Answers 1

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It is true that $\dfrac{-1}{n}< 0$ for all $n \in \mathbb{N}$. It is also true $\dfrac{-1}{n}\le 0$ that for all $n \in \mathbb{N}$. Moreover, since $\dfrac{-1}{n}$ is never zero, the statements are equivalent.

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    What do you mean with the equivalence of these statements? They are both true, but they are independent of any variables.2011-09-25