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I don't like how 0 is used as three different symbols in the beginning: the number, the point of infinity and the identity element. I know 0 is a common symbol for each of the three cases respectively but in the same context it feels rather confusing. Is that a common thing to do?


Yes, it's a very common thing to use the same symbol to mean different things in mathematics.


the number zero is always defined as being an additive identity element, and in these groups 0 is the point at infinity.




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