Why is Möbius so hard to pronounce? Aarrrgghh. I am sorry, Germans, that I have butchered the pronunciation there, although I did try my best. If anyone can teach me how to pronounce it more easily, tell me in the comments! By the way, I also just realised that Riemann should be pronounced different from what I am doing here, but I couldn't pronounce the 'r's too well, so I defaulted this to the English 'r'. Subscribe to know when I upload a new video in the series, and if you want to, and can afford to, support this channel on Patreon: www.patreon.com/mathemaniac
Hey friend, I wouldn't worry too much about it, it is not super important. But if you want a tip for "ö", think of the "i" in bird, but with rounded lips
I've recently found this channel but God am I glad I stuck around. I very much look forward to this series and thank you so much for dedicating the time and effort needed to complete these wonderful videos! I wish you nothing but the best.
I have my complex analysis exam in a week and I must say studying the topic over the last semester was incredible. There was no single lecture which failed to amaze me
One of my favorite applications of complex analysis is using the inverse-z transform (complex integral) to find the "best-fit" time-domain filter coefficients (DSP) for a specified filter frequency response, and filter order. Evaluating these complex integrals using Cauchy's Residue Theorem and complex derivatives always seems like magic.
Damn bro i am so glad i found this account. Keep up the videos man even if they dont pay of now. people will still be watching them in 5 years to pass their exams. Keep up the good work!
great - i'm looking forward to it. i've seen a handful of introductions to complex analysis and only much later when i learned some vector calculus, i realized: hey, this whole subject of complex analysis would have been much easier to understand, if it would have been treated from a 2D vector-field perspective (especially the path integrals). i hope to see also some connections to potential theory....staying tuned....
Adding myself to the list of commenters who swear by Needham's book! It really is the best Looking forward to locally amplitwist the complex plane many times in this series :)
dude complex analysis seems so cool. In my civil engineering program the last time we touched anything with complex numbers was our introductory circuits course in first year lmao so this should be cool!
I am very excited for this series. I was thinking about starting Complex Analysis at my Uni, but I am still not 100% sure about it. Hope these videos would help me. Greetings from Rome!
@@PunmasterSTP I didn't. My Uni alternates the professor who teaches the course: on one year there's a geometry professor (so the course is going to be a lot more about geometry and topology); and the other year there's an analysis professor. This year there was a geometry professor, but I am a lot more into analysis and applications. So I decided to take it next year.
Wow complex analysis is one of my favourite topics which I want to get into more depth. Plus, (reasonable) lack of rigor is actually quite good, as my motto always is "Intuition first, rigor later". Plus I'm excited that you are going to use Needham's book as a base, I read the first two chapters and I love it!
Re: Möbius: The ö sound in German is somewhere between an 'o' and 'e' sound. So, what's the best English approximation? Rarely, in parts of the USA with lots of German immigrants, people will pronounce it as "Maybius" (like the month May). But elsewhere in the USA - and in all the places I've been in - it's simply pronounced "Moh-bius" (like the name Moby Dick). I think "Moh-bius" would be the most familiar pronunciation for your audience. EDIT: Also, Riemann should be "REE-mahn"
This is his Wikipedia page (English Wikipedia): en.wikipedia.org/wiki/August_Ferdinand_M%C3%B6bius This is the IPA (International Phonetic Alphabet) transcription from the lead section of the article: UK: /ˈmɜːbiəs/, US: /ˈmeɪ-, ˈmoʊ-/;[1] German: [ˈmøːbi̯ʊs] According to that, - that "Maybius" (/ˈmɜːbiəs/ or /ˈmeɪbiəs/) is actually a UK or US pronunciation IN ENGLISH, - that "Moh-bius" (/ˈmoʊbiəs/) is a US pronunciation IN ENGLISH, - the Standard German pronunciation is transcribed in the IPA as [ˈmøːbi̯ʊs], where the German ö corresponds to the IPA vowel ø which is called the "close-mid front rounded vowel". You can have a listen of the "close-mid front rounded vowel" here: en.wikipedia.org/wiki/Close-mid_front_rounded_vowel So the "Maybius" and "Moh-bius" are ENGLISH pronunciations of the name Möbius, while, if you want the Standard German pronunciation of Möbius (which is consistent with the pronunciation rules of Standard German) like a native German speaker would say it, you would have to go with [ˈmøːbi̯ʊs]. (Or maybe you could go with some close approximation of it that /ˈmøːbi̯ʊs/ so you could account for the regional variants of German, but I don't know enough to speak on that.)
For Mobius pronunciation as in Europe, (I can't seem to type the "o" with umlaut), try saying "ee"(as in "feet") with your mouth formed to say "oo" as in "coo". Resembles the "u" in the French "rue" (street). Some even say it with a little "r" : "Mo(r)bius" (e.g. Walter Pidgeon's character in "Forbidden Planet". Americans seems to say it as written ("Mo(e) bius").
Thank you very much! Your videos are awesome! What do you think about a video on the Riemann hypothesis, which goes a little bit deaper as other "mainstream" channels?
@@mathemaniac also i submited multivariable calculus , not the one you covered before , you covered 2 inputs - 2 outputs functions. anyway i like these topics!
I will, just *at some point*, because I have to make videos to build up, and Laurent series would be the sort of things that get rolled into visualising complex integration, so appreciate your patience in the meantime.
What bothers me (at least the course I have) the exercise sessions of this subject are nothing but "prove" or "show that" kinda exercises. Nothing concrete that you can calculate. 😥
The explanation isn't actually that long to make it into a series, and to be honest, too similar to a textbook that wouldn't fit the style of this channel. Unless, as always, I can find a unique enough take on it.
@@ChechoColombia1 Most texts on real analysis will have a construction of the reals, either by Dedekind cuts or Cauchy sequences. It's quite tedious though tbh. I prefer just thinking about the reals in terms of their properties.
Glad to hear the enthusiasm! However, although I will make them as quickly as possible, each video does take a very long time, so appreciate your patience in the meantime.
Can you do a rigours version of the group theory derivation of e^ai that 3blue1brown did a video on. It was an amazing video but I have tried myself and failed to make it rigorous and searched online as well but I didn’t find anything. I would sleep much better at night if you could FULLY explain his argument. I’m loosing hope. 🥺
Glad that you are looking forward to it! I will make it as quickly as possible but still, it might not be like weekly or something - each video will take a long time to make!
I might be wrong, but this could work: ua-cam.com/video/PvUrbpsXZLU/v-deo.html P.S. A piece of advice: make video 1.5 times faster, I speak very slowly)
it's hilarious that mathematicians worry about being rigorous when they accept notions like 1+1 is always 2 despite the fact that most of mathematics exists specifically because 1+1 has no general solution. for instance: 1 dog +1 dog = 2 dogs; so 1+1=2, this is the case which Whitehead and Russell ‘proved’ in 1910 in a publication whose methodology was so shoddy that it was the hallmark example of incompleteness considered by Kurt Godel 1 dog +1 quail = 2 wings; so 1+1=2, because 1=0 and 1=2, so 0+2 = 2, and this 1+1=2 is false under PA 1 dog +1 quail = 6 legs; so 1+1=6 1 foot +1 yard = 48 inches; so 1+1=48, because of unit conversion 1 half +1 third = 5 sixths; so 1+1=5, because of fraction addition 1 frog +1 pond = 1 pond; so 1+1=1, because frogs live in ponds 1 stone +1 mountain = 1 mountain; so 1+1=1, because mountains are made of stones 1 C water +1 C dirt < 2 C mud; so 1+1 is between 1 and 2, because fluids fill gaps between granulated solids 1x +1y cannot be simplified; so 1+1 is undefined, because of like terms 1 +1i does not have length 2; so 1+1 is not 2, because of complex vectors you also have historical examples of mathematicians citing rigor as a reason to ignore correct, but new, ideas. the French were particularly good at this for some reason, with Decartes rejecting complex vectors so hard that everyone now calls the dimensional unit of the axis perpendicular to the plain vectors, 'imaginary', and the plain vectors themselves 'Real'. this is a problematic nomenclature for a number of reasons, but one of them is that Euler used 'real' in a sense which excluded infinities and infinitesimals, and then under Dedekind Completeness this later gives the absurd claim that the Reals are simultaneously Archimedean and continuous, which (apart from those two properties being mutually exclusive, which renders this false a priori) is trivially falsified by considering the asymptotic behavior of f(x) = 1/x in the neighborhood of x=0. here we can plainly see that: lim x->0+ 1/x = positive infinity 1/0 is undefined lim x->0- 1/x = negative infinity which means that, contrary to Euler, 1/0 is not itself infinite, but 1/x where x is an immediate neighbor to 0, continuous with 0, is infinite. and because these immediate neighbors to 0 are distinct from 0 itself, they carry sign, and convey this sign to their inverses. the problem here is that this unambiguously means that infinitesimals exist on the Real axis, but infinitesimals are not Archimedean. so Dedekind Completeness must be false. and this is actually apparent just from noting the nature of Dedekind's own proof which leverages Dedekind Cuts, since his basic claim is that cutting the Real axis on either side of some specified value yields the same exact cut. and this quite obviously means that Dedekind Cuts assign the name of the specified value to at least 3 distinct values, which violates identity. but this is brushed off as being acceptable because 2 of those values are infinitesimally close to the specified value. but it's even worse than just this, because Decartes' mistrust of negative numbers was still in vogue when Evariste Galois tried to present what would later become Galois Theory, and he was rejected as not being sufficiently rigorous in part because he was working with negative values in ways that mainstream French mathematicians did not accept. and quite interestingly George Peacock's 1830 publication which finally outlines how to work with negative numbers specifically addresses the asinine attitudes of the French, and this in combination with George Boole's later work on formal logic begat a movement which became Logicism, itself later giving us such ludicrously anti-rigorous delights as Dedekind Completeness and Prinicpia Mathematica. if you haven't, you should read the intro to PM and note how arrogant Whitehead and Russell were. it's absurd that they were so arrogant at all, but it's especially ludicrous given that we now live in a time where it's known that they failed in their goals that they so brazenly asserted they were uniquely equipped to achieve.
I hate making this comment because I don't know how to make it sound appropriate or even have the right to suggest. Maybe I'm the one with the problem, but it doesn't matter because nothing I say could contradict the first thing I wrote. Here is the purpose of the comment: Your voice is difficult for me, I wish it was a typical male voice or it didn't sound like that. At least that way or the tone of speaking does not appeal to my rational part, it seems to me that it contrasts with the subjects (mathematics). I know the typical response would be: take it or leave it, or you don't have to be here, etc. But in any case it is a shame, because it is unfair to ask you to change just to accommodate other/s. Well these days no one is willing to patronize, maybe me in the end. This comment will only annoy you once.
Thanks so much for the honesty. However, as you said, there isn't much that I could do. If you really find the voiceover really annoying, by all means, mute it, and I always have subtitles on my videos.
@@mathemaniac I think my problem is lack of adaptation, and that problem with exposure and interaction disappears. I love your content❤. And the fact that you've interacted with one creates a certain bond. Keep it up, keep being you!😎👍
Why is Möbius so hard to pronounce? Aarrrgghh. I am sorry, Germans, that I have butchered the pronunciation there, although I did try my best. If anyone can teach me how to pronounce it more easily, tell me in the comments! By the way, I also just realised that Riemann should be pronounced different from what I am doing here, but I couldn't pronounce the 'r's too well, so I defaulted this to the English 'r'.
Subscribe to know when I upload a new video in the series, and if you want to, and can afford to, support this channel on Patreon: www.patreon.com/mathemaniac
First reply! I'm hyped to see this series: you are so good at explaining... Keep up the good work!
Hey friend, I wouldn't worry too much about it, it is not super important. But if you want a tip for "ö", think of the "i" in bird, but with rounded lips
Thanks for the enthusiasm!
Ok thanks!
i heard that someone recently claimed to proof reimens hypothesis is it true if yes please elaborate the topic
You are insane! Couldn't have asked for another "essence of" series yet you still deliver. Thanks for the quality videos.
Thanks for the appreciation!
I thought this was my comment for a sec
@@timmydirtyrat6015 🤣
I've recently found this channel but God am I glad I stuck around. I very much look forward to this series and thank you so much for dedicating the time and effort needed to complete these wonderful videos! I wish you nothing but the best.
Thanks for the kind words and enthusiasm towards the series!
@@mathemaniac You deserve it
The real Walter White would already know complex analysis
@@turnerburger Aw damnit, you caught me. I’m Jesse and I stole Walter’s phone
Ibidem
I have my complex analysis exam in a week and I must say studying the topic over the last semester was incredible. There was no single lecture which failed to amaze me
I know it's been awhile, but how did your exam go?
Are you a pure math student ?
One of my favorite applications of complex analysis is using the inverse-z transform (complex integral) to find the "best-fit" time-domain filter coefficients (DSP) for a specified filter frequency response, and filter order. Evaluating these complex integrals using Cauchy's Residue Theorem and complex derivatives always seems like magic.
Thank you so much for doing this series, I can't wait to see it!
Hope you will enjoy it!
I look forward to your forthcoming series. Sounds like a great refresher set of videos.
Damn bro i am so glad i found this account. Keep up the videos man even if they dont pay of now. people will still be watching them in 5 years to pass their exams. Keep up the good work!
Thanks so much for the compliment!
I've finally started learning some complex analysis recently after having heard about how cool it is for so long. Very convenient timing!
THIS is a series I am getting around! Wow, thank you!
great - i'm looking forward to it. i've seen a handful of introductions to complex analysis and only much later when i learned some vector calculus, i realized: hey, this whole subject of complex analysis would have been much easier to understand, if it would have been treated from a 2D vector-field perspective (especially the path integrals). i hope to see also some connections to potential theory....staying tuned....
Took a course on complex analysis last year, but I’m still excited to watch this. It’ll be a good refresher!
Adding myself to the list of commenters who swear by Needham's book! It really is the best
Looking forward to locally amplitwist the complex plane many times in this series :)
Yes the book is really good!
I first read that as 'armtwist'. I guess it does about the same to that plane!
dude complex analysis seems so cool. In my civil engineering program the last time we touched anything with complex numbers was our introductory circuits course in first year lmao so this should be cool!
Yes! Complex analysis is really cool!
Complex analysis? More like "Completely amazing this is!" Thanks for creating a wonderful series, and I'll most certainly be watching until the end.
Wow! I've always thought that Needham's book should be animated in some series like this! Awesome stuff :)
Yes, that's what I think as well!
Thank you so much for this!! Really looking forward to the rest of the series
Glad to see the enthusiasm of this series!
damn! super excited for this series! it will be a really nice complement to the courses at universities in terms of visualisation and understanding!
Glad to know the enthusiasm of this series!
How's university been going?
I am very excited for this series. I was thinking about starting Complex Analysis at my Uni, but I am still not 100% sure about it. Hope these videos would help me. Greetings from Rome!
Glad to see the enthusiasm!
I'm just curious. Did you end up taking the class?
@@PunmasterSTP I didn't.
My Uni alternates the professor who teaches the course: on one year there's a geometry professor (so the course is going to be a lot more about geometry and topology); and the other year there's an analysis professor.
This year there was a geometry professor, but I am a lot more into analysis and applications. So I decided to take it next year.
@@frei6833 That's interesting to know, and I hope the class goes well next year.
@@PunmasterSTP Thanks👍🏼❤️
Thank you, just what i needed
Wow thanks! Hope you will like both the group theory series and this one!
Hello , your that video of impossible integral was super insane !
Thank you for this. I loved your group theory videos, looking forward to complex analysis :)
Thanks so much for the kind words!
I appreciate the MATHEMANIAC channel for this effort.
Thanks!
LOVE IT!!!! I think a few example problems would be great
Wow complex analysis is one of my favourite topics which I want to get into more depth. Plus, (reasonable) lack of rigor is actually quite good, as my motto always is "Intuition first, rigor later". Plus I'm excited that you are going to use Needham's book as a base, I read the first two chapters and I love it!
Glad to see the enthusiasm of this series!
Wow, those animations look sharp, this is gonna be good!
Hope you will enjoy the series
Looking forward to it! This channel is simply great
Good to see the enthusiasm towards the series!
Thanx for wetting my appetite for this fascinating subject!
Re: Möbius:
The ö sound in German is somewhere between an 'o' and 'e' sound. So, what's the best English approximation?
Rarely, in parts of the USA with lots of German immigrants, people will pronounce it as "Maybius" (like the month May). But elsewhere in the USA - and in all the places I've been in - it's simply pronounced "Moh-bius" (like the name Moby Dick). I think "Moh-bius" would be the most familiar pronunciation for your audience.
EDIT: Also, Riemann should be "REE-mahn"
Morbius
This is his Wikipedia page (English Wikipedia):
en.wikipedia.org/wiki/August_Ferdinand_M%C3%B6bius
This is the IPA (International Phonetic Alphabet) transcription from the lead section of the article:
UK: /ˈmɜːbiəs/, US: /ˈmeɪ-, ˈmoʊ-/;[1] German: [ˈmøːbi̯ʊs]
According to that,
- that "Maybius" (/ˈmɜːbiəs/ or /ˈmeɪbiəs/) is actually a UK or US pronunciation IN ENGLISH,
- that "Moh-bius" (/ˈmoʊbiəs/) is a US pronunciation IN ENGLISH,
- the Standard German pronunciation is transcribed in the IPA as [ˈmøːbi̯ʊs], where the German ö corresponds to the IPA vowel ø which is called the "close-mid front rounded vowel".
You can have a listen of the "close-mid front rounded vowel" here:
en.wikipedia.org/wiki/Close-mid_front_rounded_vowel
So the "Maybius" and "Moh-bius" are ENGLISH pronunciations of the name Möbius, while, if you want the Standard German pronunciation of Möbius (which is consistent with the pronunciation rules of Standard German) like a native German speaker would say it, you would have to go with [ˈmøːbi̯ʊs].
(Or maybe you could go with some close approximation of it that /ˈmøːbi̯ʊs/ so you could account for the regional variants of German, but I don't know enough to speak on that.)
"Visual complex analysis" by Needham is one of my favorite
Mine too!
I cant wait to see solving real valuated integrals using Residues Theorem
That might be grouped into "applications" part, which would not be released in a very short time, but glad to know your enthusiasm towards the series!
Amazing!! I can't wait to see the next videos!
Thanks for the enthusiasm!
You have become my fav math creator after 3Blue1Brown! Thanks!
Im
Hyped!
Looking forward!
hey, i was one of the ones to request this! thanks!
I actually the finding the way to learn complex analysis from last one year... And found u... Pls do... Videos...
mention of Tristan Needham's book is enough for me to subscribe and watch all your videos
Wow thanks! That is indeed a good book!
Can’t wait!!!
Me too!
I think it has applications in control theory - particularly non-linear control systems.
looking forward to this
Me too!
For Mobius pronunciation as in Europe, (I can't seem to type the "o" with umlaut), try saying "ee"(as in "feet") with your mouth formed to say "oo" as in "coo". Resembles the "u" in the French "rue" (street).
Some even say it with a little "r" : "Mo(r)bius" (e.g. Walter Pidgeon's character in "Forbidden Planet".
Americans seems to say it as written ("Mo(e) bius").
Thank you very much! Your videos are awesome! What do you think about a video on the Riemann hypothesis, which goes a little bit deaper as other "mainstream" channels?
I subscribed just recently and glad I did. Looking forward to the next videos 👍
Awesome, thank you!
what is the prerequisite for this? i might see at as such but i don't think i could say i see myself understand it beyond analytical geometry
LETS GOOOO BOIIIIIIIIII. LETS GOOOOOO
Glad to see the enthusiasm!
Bring it on !
OMG you are the best thanks sooo much you are my hero now
Omg AWESOME!!!!!!!
Thank you sooo much!!
can't wait
Oo looking forward
thanks so much! exited to watch! :D
Hope you enjoy!
@@mathemaniac also i submited multivariable calculus , not the one you covered before , you covered 2 inputs - 2 outputs functions. anyway i like these topics!
Explica muy bien con Manim, exelente, saludo desde RD
Damn, I should've joined university a year later, just passed my complex analysis course, will watch these videos anyway :)
Hopefully you will enjoy them!
Awesome good! Thank you!
Maybe fractals is another application ;-) Its used in games/movies to limit compute (zooming in, has same structure).
Just like 3B1B but with more nerdy content, thanks
I'm currently debating on taking complex analysis or linear algebra next semester. Do you have a suggestion?
I hope I can find some applications to the life and social sciences!!! 🙏 Those are my main passions!!! ❤️
Let's do this!
Thank you so much,
Please try to visualize the Laurent series
I will, just *at some point*, because I have to make videos to build up, and Laurent series would be the sort of things that get rolled into visualising complex integration, so appreciate your patience in the meantime.
uhulllllll!! 🤸🤸🤸🤸💥 😵🥴🙃❤️
Are you and Grant Sanderson(3Blue1Brown) related?🙂
Haha no... but the visual style is inspired by him!
What bothers me (at least the course I have) the exercise sessions of this subject are nothing but "prove" or "show that" kinda exercises.
Nothing concrete that you can calculate.
😥
Good job ❤️❤️❤️❤️❤️lots of 💕
I cant wait to watch them
Awesome Thanks!
Thank you !
Thank you so much!!!
Thank you so much🙏🙏
THANK YOU!!!
You should do a series constructing real numbers with cauchys sequences.
The explanation isn't actually that long to make it into a series, and to be honest, too similar to a textbook that wouldn't fit the style of this channel. Unless, as always, I can find a unique enough take on it.
@@mathemaniac thank you, I really like the way you explain. In which text book can I find a complete construction of the real set?
@@ChechoColombia1 Most texts on real analysis will have a construction of the reals, either by Dedekind cuts or Cauchy sequences. It's quite tedious though tbh. I prefer just thinking about the reals in terms of their properties.
Please upload videos as soon as possible
Glad to hear the enthusiasm! However, although I will make them as quickly as possible, each video does take a very long time, so appreciate your patience in the meantime.
Tantalizing indeed!
If something provide an opportunity to show off, I'll take it.
Haha :)
Which aplication is used bro.
Can you do a rigours version of the group theory derivation of e^ai that 3blue1brown did a video on. It was an amazing video but I have tried myself and failed to make it rigorous and searched online as well but I didn’t find anything. I would sleep much better at night if you could FULLY explain his argument.
I’m loosing hope. 🥺
Taylor series
🔥🔥🔥
im so glad a hongkonger makes great math videos
Thank you so much sir for making this video :-)
Amazing
Thank you
Can you believe that in romanian physics universities, this part of math is not treated? How?! How would you do physics without complex analysis?!
I want to enjoy with complex analysis
Hope you will do so with this series!
Nice!
Thanks!
Video 2: to get everyone on the same plane, for the mathematically pun inclined.
Haha
Sir make it fast please
Glad that you are looking forward to it! I will make it as quickly as possible but still, it might not be like weekly or something - each video will take a long time to make!
This is going to be art...*eh um* I mean...good.
Awww thanks!
Niceeeee
Niceeee
Complex analysis
L I F E S A V E R
The music at the end sounds like Lutheran church music
+
i am simple physicist is see complex analysis i like the video =0
I might be wrong, but this could work: ua-cam.com/video/PvUrbpsXZLU/v-deo.html
P.S. A piece of advice: make video 1.5 times faster, I speak very slowly)
Is this Bruce Lee? Sounds like Bruce Lee, just sayin.
it's hilarious that mathematicians worry about being rigorous when they accept notions like 1+1 is always 2 despite the fact that most of mathematics exists specifically because 1+1 has no general solution. for instance:
1 dog +1 dog = 2 dogs; so 1+1=2, this is the case which Whitehead and Russell ‘proved’ in 1910 in a publication whose methodology was so shoddy that it was the hallmark example of incompleteness considered by Kurt Godel
1 dog +1 quail = 2 wings; so 1+1=2, because 1=0 and 1=2, so 0+2 = 2, and this 1+1=2 is false under PA
1 dog +1 quail = 6 legs; so 1+1=6
1 foot +1 yard = 48 inches; so 1+1=48, because of unit conversion
1 half +1 third = 5 sixths; so 1+1=5, because of fraction addition
1 frog +1 pond = 1 pond; so 1+1=1, because frogs live in ponds
1 stone +1 mountain = 1 mountain; so 1+1=1, because mountains are made of stones
1 C water +1 C dirt < 2 C mud; so 1+1 is between 1 and 2, because fluids fill gaps between granulated solids
1x +1y cannot be simplified; so 1+1 is undefined, because of like terms
1 +1i does not have length 2; so 1+1 is not 2, because of complex vectors
you also have historical examples of mathematicians citing rigor as a reason to ignore correct, but new, ideas. the French were particularly good at this for some reason, with Decartes rejecting complex vectors so hard that everyone now calls the dimensional unit of the axis perpendicular to the plain vectors, 'imaginary', and the plain vectors themselves 'Real'. this is a problematic nomenclature for a number of reasons, but one of them is that Euler used 'real' in a sense which excluded infinities and infinitesimals, and then under Dedekind Completeness this later gives the absurd claim that the Reals are simultaneously Archimedean and continuous, which (apart from those two properties being mutually exclusive, which renders this false a priori) is trivially falsified by considering the asymptotic behavior of f(x) = 1/x in the neighborhood of x=0. here we can plainly see that:
lim x->0+ 1/x = positive infinity
1/0 is undefined
lim x->0- 1/x = negative infinity
which means that, contrary to Euler, 1/0 is not itself infinite, but 1/x where x is an immediate neighbor to 0, continuous with 0, is infinite. and because these immediate neighbors to 0 are distinct from 0 itself, they carry sign, and convey this sign to their inverses.
the problem here is that this unambiguously means that infinitesimals exist on the Real axis, but infinitesimals are not Archimedean. so Dedekind Completeness must be false. and this is actually apparent just from noting the nature of Dedekind's own proof which leverages Dedekind Cuts, since his basic claim is that cutting the Real axis on either side of some specified value yields the same exact cut. and this quite obviously means that Dedekind Cuts assign the name of the specified value to at least 3 distinct values, which violates identity. but this is brushed off as being acceptable because 2 of those values are infinitesimally close to the specified value.
but it's even worse than just this, because Decartes' mistrust of negative numbers was still in vogue when Evariste Galois tried to present what would later become Galois Theory, and he was rejected as not being sufficiently rigorous in part because he was working with negative values in ways that mainstream French mathematicians did not accept. and quite interestingly George Peacock's 1830 publication which finally outlines how to work with negative numbers specifically addresses the asinine attitudes of the French, and this in combination with George Boole's later work on formal logic begat a movement which became Logicism, itself later giving us such ludicrously anti-rigorous delights as Dedekind Completeness and Prinicpia Mathematica.
if you haven't, you should read the intro to PM and note how arrogant Whitehead and Russell were. it's absurd that they were so arrogant at all, but it's especially ludicrous given that we now live in a time where it's known that they failed in their goals that they so brazenly asserted they were uniquely equipped to achieve.
I hate making this comment because I don't know how to make it sound appropriate or even have the right to suggest.
Maybe I'm the one with the problem, but it doesn't matter because nothing I say could contradict the first thing I wrote. Here is the purpose of the comment:
Your voice is difficult for me,
I wish it was a typical male voice or it didn't sound like that.
At least that way or the tone of speaking does not appeal to my rational part, it seems to me that it contrasts with the subjects (mathematics).
I know the typical response would be: take it or leave it, or you don't have to be here, etc.
But in any case it is a shame, because it is unfair to ask you to change just to accommodate other/s. Well these days no one is willing to patronize, maybe me in the end.
This comment will only annoy you once.
Thanks so much for the honesty. However, as you said, there isn't much that I could do. If you really find the voiceover really annoying, by all means, mute it, and I always have subtitles on my videos.
@@mathemaniac
I think my problem is lack of adaptation, and that problem with exposure and interaction disappears.
I love your content❤. And the fact that you've interacted with one creates a certain bond.
Keep it up, keep being you!😎👍