I'm about to go off-line so I can't enter a protracted discussion, but your comment leaves me completely baffled. For example, you say:

We know that some functions don't converge but that's only because we can't try n infinite numbers.

That's just patently false. For example, we know that this sequence doesn't converge:

1,

1 + 1/2,

1 + 1/2, + 1/3,

1 + 1/2, + 1/3 + 1/4,

1 + 1/2, + 1/3 + 1/4 + 1/5,

... etc.

We know that won't converge, and not being able to try infinite numbers has nothing to do with it.

So what you say seems to me to be, on the surface, pretty much complete nonsense. To one who is trained in mathematics, what you're saying feels very similar to people who haven't travelled much saying that the Earth is obviously flat.