4 ms·

> the ubiquitous IEEE floating-point standard defines two numbers to represent zero, the positive and the negative zeros. Seriously, how did anyone think inclu

> the ubiquitous IEEE floating-point standard defines two numbers to represent zero, the positive and the negative zeros. Seriously, how did anyone think including two fantasy numbers was a good idea? Not to mention excluding the real zero.

westurner 3y ago
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.
- beardyw 3y ago
  I remember a system I was working on where I was setting up an empty financial account. Error - no currency specified. Well a) I don't have a currency, but more importantly b) how does nothing need a currency? It's as if a farmer had a field with no animals in it and was asked what sort of animals it hasn't got in it. I think the Romans were right.

westurner 3y ago

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.

beardyw 3y ago
I remember a system I was working on where I was setting up an empty financial account. Error - no currency specified. Well a) I don't have a currency, but more importantly b) how does nothing need a currency? It's as if a farmer had a field with no animals in it and was asked what sort of animals it hasn't got in it. I think the Romans were right.