Complex Analysis 25 | Cauchy's Theorem (general version)

[@elitewarrior689]

Whoa...! After all these years, your face appear on the video, thanks Sir for giving us a figure to remember and refer to whenever we encounter difficulties in Mathematics.

[@brightsideofmaths]

My pleasure

[@nirmalbajiya3283]

Hello sir I am from INDIA and I am a BTech student in IIT Kanpur one of the most premiere engineering institutes around the country still I was not able to understand the concept by studying from our professor but you're such a wonderful teacher that you explained everything from basic to the core.Thank you So much sir

[@brightsideofmaths]

Thank you very much :) I am happy that I can help here!

[@eamon_concannon]

I have considerable familiarity with most of what you cover in this playlist. However, I enjoy getting your take on this subject, which I think is one of the most interesting of mathematical subjects. Subscribed and considering membership.

[@brightsideofmaths]

Thank you very much! I am always happy about support :)

[@zwazwezwa]

No way I imagined you look like this. Great look sir!

[@brightsideofmaths]

Thanks! Everyone thinks that I am old ;)

[@zwazwezwa]

​@@brightsideofmaths It's how about we feel, even Adonis is old ;) Cheers, thanks for the reply

[@malawigw]

Math Pokemon: gonna cauchy them all

[@nm-de3bw]

Couldn't we just aproximate the closed curve integral with closed polygon integrals and show that in the limit the value is still 0?

[@brightsideofmaths]

Yes, a polygon path is enough. You can see that in the pdf version of the video.

[@yololololo9081]

i had an off topic doubt related to foundations of mathematics, ive noticed that logic uses notions of set theory for its axioms and set theory uses logic in a similar way, isnt this a kind of circular reasoning? and ive always been told that circular reasoning is generally "bad". how should i be thinking about this? it bugs me a lot.

[@brightsideofmaths]

The shortest answer would be that you formulate logic and the axioms of set theory simultaneously. Then you don't have a circular reasoning and a foundation for mathematics. The longer answer would have to deal with a lot of logical formulations that don't need the axioms of set theory.

[@gutzimmumdo4910]

logic is the framework of philosophy, set theory derives from logic not the otherway around.

[@yololololo9081]

@@brightsideofmaths thanks for the response, i did some research and turns out we can use two notions of sets, one in the meta-language which is used to construct logic and then we can use this logic to construct axiomatic set theory. so technically it's not circular reasoning because we have two different kinds of set, a naive/informal one and an axiomatic one, both independent concepts.

[@yololololo9081]

@@gutzimmumdo4910 not really. logic, especially second order logic uses notions of sets in it's construction, but this set isnt the same as the zfc set which is developed later, so there's no circular reasoning.

[@gutzimmumdo4910]

@@yololololo9081 the consept of a "set", "bundle","list","colection","bagg" etc was used far back before zfc was a formulated. ZFC Set theory is just a type of logic that uses certain axioms suited to construct the natural numbers, altou, ZFC is not the only framework u can use for the fundamentals, its just a bunch of axioms/assumptions based on what we alrady know from logic, btw when i say logic i dont mean mathematical logic, i mean Logic the branch of philosophy.

[@hyperduality2838]

Inside is dual to outside, interior is dual to exterior. Union is dual to intersection. Convex (convergent, syntropy, homology) is dual to concave (divergent, entropy, co-homology). Inclusion is dual to exclusion -- the Pauli exclusion principle for Fermions. Bosons (inclusion or the same state) are dual to Fermions (exclusion or different states) -- atomic duality! Waves are dual to particles -- quantum duality. "Always two there are" -- Yoda.