2 ms·

Addition, multiplication, and division can be emulated with subtraction. so how are they fundamental? Take tetration, for example, it fulfills all criteria of

• deleted 3y ago
  [deleted]
• eru 3y ago
  Talking about addition, subtraction, multiplication and division as fundamental operations is just to capture the imagination of the layman. Modern mathematics talks more abstractly. A mathematician would probably talk about addition, multiplication and inverse being fundamental operations. You can't, in general, emulate multiple with addition (nor with subtraction). Yes, for integers you can view multiplication as repeated addition. But that's not true for general structures. Have a look at eg https://en.wikipedia.org/wiki/Tropical_semiring https://en.wikipedia.org/wiki/Tropical_semiring for some inspiration. You can apply tropical semirings to shortest path problems in graphs: https://cs.nyu.edu/~mohri/pub/jalc.pdf https://cs.nyu.edu/~mohri/pub/jalc.pdf
  • psychoslave 3y ago
    Meh, don’t you had the memo that it’s all about the endogenic structure of the identity function within a toroidal network topology plunged within the diagonal of a transcendental mesh? Just kidding, but not that stretched from what can easily find in contemporary mathematical publications.
• fxj 3y ago
  I wonder how a society would have developed if they would have invented the log function before multiplication. log(a*b) = log(a) + log(b) Also the log function comes very natural from the human senses, e.g. exponential scale of the musical tones, sound amplitude measured logarithmically, the eye works logarithmically too. just my 2 ct