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Explanation for why $1\neq 0$ is explicitly mentioned in Chapter 1 of Spivak's Calculus for properties of numbers.
I am self-studying the wonderful book, Elementary Geometry from an Advanced Standpoint.
In chapter 1, problem 18 it says: Postulate M-6 (which says 1 not equal to 0
) may seem superfluous. Is it? Can it be proved, on the basis of the other postulates, that there is any number at all other than 0?
The "other postulates" include the commutativity, associativity, identity, and distributive laws for addition and multiplication.
I don't see how to show that without the postulate 1 not equal to 0
it cannot be shown that there is any number other than 0. Would you help please?