Sequences and Nets: Does (1/n) Converge to [0,1]?

[ForMyThunder]

Say the real numbers were given a topology \left\{R,\phi, [0,1]\right\}. Does the sequence (1/n) converge to every point of [0,1] since it is a neighborhood of every point?

 

[Fredrik]

What is R and \phi? Does your topology satisfy the definition of a topology?

 

[micromass]

If \mathbb{R} has the topology \{\emptyset,[0,1],\mathbb{R}\}, then the sequence (1/n) converges to every point of \mathbb{R}!

 

[ForMyThunder]

If \mathbb{R} has the topology \{\emptyset,[0,1],\mathbb{R}\}, then the sequence (1/n) converges to every point of \mathbb{R}!

Yeah, I guess you're right. Thanks.