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So exp(0) is necessarily undefined?
There's no ‘necessarily’ about it. You can have a subtle situation where 0⁰ is defined in some contexts and undefined in others; lots of notation is like that. But it's not necessary. It's not necessary that operations be continuous. For that matter, it's not necessary that power series be written to begin at 0; you could begin them at 1 and write the order-0 term separately.
In any case, Oscar is correct that there are textbooks out there that firstly state that 0⁰ is undefined and also write power series beginning at 0. I'm teaching from one right now. (They actually take care to write the order-0 term separately when they first introduce the concept, but later they forget.)
TobyBartels
npub1kp…gr9jw
2025-06-14 17:21:04 UTC
in reply to nevent1q…ym8z
Author Public Key
npub1kpf5nh0jvj3ygrlz3zw2s2qvy2dpdp5zdlwnl2nqujugfugumkfqngr9jwPublished at
2025-06-14 17:21:04 UTCEvent JSON
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