Addition, multiplication, and division can be emulated with subtraction. so how are they fundamental?
Take tetration, for example, it fulfills all criteria of being "fundamental" as multiplication. but isn't listed as such
Take tetration, for example, it fulfills all criteria of being "fundamental" as multiplication. but isn't listed as such
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 for some inspiration. You can apply tropical semirings to shortest path problems in graphs: https://cs.nyu.edu/~mohri/pub/jalc.pdf
Just kidding, but not that stretched from what can easily find in contemporary mathematical publications.
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