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And other people care about natural numbers being the set of cardinal numbers for finite sets. Others want the set of natural numbers with addition to be a mono
by yakubin 8y ago
And other people care about natural numbers being the set of cardinal numbers for finite sets. Others want the set of natural numbers with addition to be a monoid. And actually most-known series in analysis are usually indexed starting from zero, because that's when the formulas are usually simpler.
- traderjane 8y agoBut if you asked the same people to build the naturals, they'd likely include an initial object that behaves like 0.
- rocqua 8y agoI fully agree. However, there is also pushback on ordinals vs cardinals, and monoids vs semigroups.