this post was submitted on 07 Sep 2024
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Science Memes

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submitted 2 months ago by [email protected] to c/[email protected]
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[–] [email protected] 3 points 2 months ago (1 children)

i still feel like this whole ε-δ thing could have been avoided if we had just put more effort into the “infinitesimals” approach, which is a bit more intuitive anyways.

but on the other hand, you need a lot of heavy tools to make infinitesimals work in a rigorous setting, and shortcuts can be nice sometimes

[–] [email protected] 8 points 2 months ago (1 children)

Infinitesimal approach is often more convoluted when you perform various operations, like exponentials.

Instead, epsilon-delta can be encapsulated as a ball business, then later to inverse image check for topology.

[–] [email protected] 1 points 2 months ago

i think the ε-δ approach leads to way more cumbersome and long proofs, and it leads to a good amount of separation between the “idea being proved” and the proof itself.

it’s especially rough when you’re chasing around multiple “limit variables” that depend on different things. i still have flashbacks to my second measure theory course where we would spend an entire two hour lecture on one theorem, chasing around ε and η throughout different parts of the proof.

best to nip it in the bud id say