Post Closed as "not a real question" by Chris Godsil, Steven Landsburg, Henry Cohn, quid, Benjamin Steinberg

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What constitutes the division between discrete and non-discrete math? Are there any math subject where it's being blurred?

I often heard about this division but always in a non-formal manner. What constitutes it? Is it a limit operation? Or a fundamental distinction between countable and uncountable sets? And what math subjects can be accurately attributed to one or another type?

I really find this division very weird.