definition limit from above equivalent notations

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Given:

$$ \lim_{x\to1+}f(x)= +\infty $$ Formulate the limit definition.

I have two candidates and was wondering if they were both correct and indeed equivalent.

1)$$ \forall M>0, \exists \delta>0 \text{ such that whenever, } 0< x-1< \delta, \text{we have that} f(x)>M $$ Or alternatively

2)$$ \forall M>0, \exists \delta>0 \text{ such that whenever, } x \in (1, 1+ \delta), \text{we have that} f(x)>M $$