I don't think you can have a ring or a field without additive inverses. Additive inverse: https://en.wikipedia.org/wiki/Additive_inverse https://en.wikipedia.o

I don't think you can have a ring or a field without additive inverses. Additive inverse: https://en.wikipedia.org/wiki/Additive_inverse https://en.wikipedia.org/wiki/Additive_inverse : > For a number (and more generally in any ring), the additive inverse can be calculated using multiplication by −1; that is, −n = −1 × n. Examples of rings of numbers are integers, rational numbers, real numbers, and complex numbers Must there be an additive inverse of zero? There was no concept of zero in early mathematics or in Roman numerals. 0 (number) https://en.wikipedia.org/wiki/0 https://en.wikipedia.org/wiki/0 Division by signed or unsigned zero is undefined with Integers, Rationals, and Reals. 1/x is not equivalent to 2/x at any point other than x=0, where their signed tendency is toward a limit with positive and/or negative infinity. IEEE-754 also specifies only three infinities: positive, negative, and unsigned. Conway's surreal infinities are multiple. Fairly, aren't there infinity infinities? Infinity_n. Perhaps one for each different symbolic value, but which cancel out as multiplicative inverses? If 1/x != 2/x at any real point, it defies intuition that their limits are equally -/+ infinity.