5 ms·
Basically, either you have unsigned numbers (conjugated magnitude), with growth/shrink operations, or you have numbers with a polarity, with displacement operat
by xeonmc 3y ago
Basically, either you have unsigned numbers (conjugated magnitude), with growth/shrink operations, or you have numbers with a polarity, with displacement operations .
It is incomplete to have the notion of "negative numbers" without also including the imaginary parts.
- jojobas 3y agoIt's only incomplete if you require particular operations, you're perfectly fine with +-*/ and real numbers.
- deleted 3y ago[deleted]
- xeonmc 3y agoIf you have real numbers instead of integers, then it implies fractional applications of the arithmetic operators. Fractional negation is complex rotation, so if you have negative numbers and they are non-integers then it necessarily must also include complex numbers.
- jojobas 3y ago> implies fractional applications of the arithmetic operators Does it? Where does this implication come from?
- xeonmc 3y agoYou can’t generate a continuum without log/exp
- jojobas 3y agoSo log/exp or partial operators? And what do you mean by "generate a continuum"? Both log and exp are formulated without the need for complex numbers. Real numbers are a field for +-/ (although not a group for / because zero is weird).