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- Inventing zero. Our own culture still has a long way to go here - we still call the first day of the month "1", and plenty of other things.
That doesn't have much to do with the invention of 0.
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- Sticking to integers. In fact, our society went from inventing continuous numbers to realising that nature is quantised in only a few millennia - you could skip that step.
We didn't, really. As far as we know, space time is still continuous. It could not be, but so far, nothing indicates it.
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- Developing things in a different order. The Greeks developed geometry earlier than what was really useful, my conpeople developed symbolic logic instead.
Geometry was mostly developed for practical reasons (it's not called "earth measuring" for no reason). And the ancient greeks did start up a bit on logic, which was also quite studied in medieval times.
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- Trivial arithmetic systems. Gödel's theorem says that a non-trivial arithmetic system can't be complete and coherent - what if your conpeople decide to go with one that's trivial?
They're gonna have a hard time doing it, because anything better than a caveman understanding of mathematics will be non-trivial, Gödel-wise (basically addition and multiplication is already too much). Also Gödel only matters if you do axiomatic mathematics, which is probably gonna come a bit after multiplication, I think.
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A complete redesign of calculus, for example, would be very interesting.
No need to look too far. There's literaly dozens of ways to define calculus in modern mathematics.
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They'll get the same value for pi that we do, but they may not give a shit that ei*pi = -1 and might, for example, not bother to work out something like complex numbers until such time as working with electricity forces it.
Hell, practical methods for what would later be complex numbers already exist in our culture. Can't remember the name, but back around the 16th-17th century, they just represented some physical quantities in R² to solve some optics problems.