I didn't down-vote you, by the way, even though I think you are mis-guided, and probably have been badly taught. From other things you've said I think you could, if it were presented well, find the whole topic intriguing.

Because, in part, you can't have the one without the other. You can't talk about limits without having a model for infinity. They are inextricably entwined, each idea leading to the other.

It's sounds to me like you've simply been put off by loads of badly written Pop-Math articles that attempt to boggle and astound, without showing the real truths as to why the whole subject is really, really cool, and simultaneously, useful and practical.