Cauchy's Functional Equations (part1: The Additive One)

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#IMO​ #FunctionalEquations​ #MathOlympiad​
In this video we start discussing the famous powerful Cauchy's Functional Equations and begin with the the additive one...!
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I upload videos concerning math Olympiad contests to help students preparing for math Olympiad and all people who share the love for some interesting math problems.
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I think that you should mention that as long as f is (strictly) increasing c can't be 0 so we can divide f by c.
Anyway, good job! useful for me!

atelieruldematematica
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gr8 video! wow so amazing! functional equations are back? are you a university student? WOW! it's amazing you can do this!!

aashsyed
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Not even an olympiad student, but I really enjoyed the video! Great job :) (although I would have loved a proof of the existence of a rational between two distinct irrationals despite its seemingly obvious truth :p)
بس في شي واحد محيرني، ليش ما تطلع تدرس برا البلد؟ 😅
سؤال من طالب بدو يفوت تحضيرية السنة الجاية بس بحب الرياضيات

bisher_
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Sir, plz give us some number theory and combinatorics class.plz, 🥺

iftekharsizan
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Does picking an arbitrary rational number between the two real numbers require the axiom of choice?

FadkinsDiet
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Excuse me, maybe I missed it from the video, but what is an example of a solution other that f(x) = x if we drop any additional condition (continuity, increasing etc.)?

Wurfenkopf
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Sorry, but why is f(0) = 0?
Let's say f(x)= x+5 -> f(0) = 0 + 5 = 5?
Or am I mistaken?

lin