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*Note: I think questions 2-4 are erroneous?

1) There does

2) The product of all reals in [tex] ( 0 , 1 ) [/tex] is zero, right?

3) The product of all reals in [tex] ( 1 , 2 ) [/tex] is infinity, right?

4) The product of all reals in [tex] (0 , \infty ) [/tex] I suppose is one, because each real greater than one has a reciprocal less than one (and vica versa). Their products equal to one. Therefore the product of all reals in [tex] (0 , \infty ) [/tex] is one?

1) There does

**NOT**exist any [tex] x \in \mathbb{R}[/tex] such that [itex] x \in \left( {1,1} \right) [/tex] ?2) The product of all reals in [tex] ( 0 , 1 ) [/tex] is zero, right?

3) The product of all reals in [tex] ( 1 , 2 ) [/tex] is infinity, right?

4) The product of all reals in [tex] (0 , \infty ) [/tex] I suppose is one, because each real greater than one has a reciprocal less than one (and vica versa). Their products equal to one. Therefore the product of all reals in [tex] (0 , \infty ) [/tex] is one?

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