Why is the number zero so important and confusing?
Zero seems simple but it causes a lot of weird situations. You can't divide by zero. Zero times anything is zero. Zero isn't positive or negative. Was zero always a number, or did someone have to 'invent' it? Why is something that means 'nothing' such a big deal in math?
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2 Answers
I'm a physics grad student and this is one of my favorite questions to explain. The key insight is that our everyday intuition doesn't always apply at extreme scales — very small (quantum), very large (cosmological), or very fast (relativistic).
This is actually a much deeper question than it appears on the surface. The simple answer most textbooks give is technically correct but misses a lot of nuance. Let me try to explain it in a way that captures the full picture.
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